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Math Word Problems

Welcome to the math word problems worksheets page at Math-Drills.com! On this page, you will find Math word and story problems worksheets with single- and multi-step solutions on a variety of math topics including addition, multiplication, subtraction, division and other math topics. It is usually a good idea to ensure students already have a strategy or two in place to complete the math operations involved in a particular question. For example, students may need a way to figure out what 7 × 8 is or have previously memorized the answer before you give them a word problem that involves finding the answer to 7 × 8.

There are a number of strategies used in solving math word problems; if you don't have a favorite, try the Math-Drills.com problem-solving strategy:

• Question : Understand what the question is asking. What operation or operations do you need to use to solve this question? Ask for help to understand the question if you can't do it on your own.
• Estimate : Use an estimation strategy, so you can check your answer for reasonableness in the evaluate step. Try underestimating and overestimating, so you know what range the answer is supposed to be in. Be flexible in rounding numbers if it will make your estimate easier.
• Strategize : Choose a strategy to solve the problem. Will you use mental math, manipulatives, or pencil and paper? Use a strategy that works for you. Save the calculator until the evaluate stage.
• Calculate : Use your strategy to solve the problem.
• Evaluate : Compare your answer to your estimate. If you under and overestimated, is the answer in the correct range. If you rounded up or down, does the answer make sense (e.g. is it a little less or a little more than the estimate). Also check with a calculator.

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What can QuickMath do?

QuickMath will automatically answer the most common problems in algebra, equations and calculus faced by high-school and college students.

• The algebra section allows you to expand, factor or simplify virtually any expression you choose. It also has commands for splitting fractions into partial fractions, combining several fractions into one and cancelling common factors within a fraction.
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Solving Word Questions

With LOTS of examples!

In Algebra we often have word questions like:

Example: Sam and Alex play tennis.

On the weekend Sam played 4 more games than Alex did, and together they played 12 games.

How many games did Alex play?

How do we solve them?

The trick is to break the solution into two parts:

Turn the English into Algebra.

Then use Algebra to solve.

Turning English into Algebra

To turn the English into Algebra it helps to:

• Read the whole thing first
• Do a sketch if possible
• Assign letters for the values
• Find or work out formulas

You should also write down what is actually being asked for , so you know where you are going and when you have arrived!

Also look for key words:

Thinking Clearly

Some wording can be tricky, making it hard to think "the right way around", such as:

Example: Sam has 2 dollars less than Alex. How do we write this as an equation?

• Let S = dollars Sam has
• Let A = dollars Alex has

Now ... is that: S − 2 = A

or should it be: S = A − 2

or should it be: S = 2 − A

The correct answer is S = A − 2

( S − 2 = A is a common mistake, as the question is written "Sam ... 2 less ... Alex")

Example: on our street there are twice as many dogs as cats. How do we write this as an equation?

• Let D = number of dogs
• Let C = number of cats

Now ... is that: 2D = C

or should it be: D = 2C

Think carefully now!

The correct answer is D = 2C

( 2D = C is a common mistake, as the question is written "twice ... dogs ... cats")

Let's start with a really simple example so we see how it's done:

Example: A rectangular garden is 12m by 5m, what is its area ?

Turn the English into Algebra:

• Use w for width of rectangle: w = 12m
• Use h for height of rectangle: h = 5m

Formula for Area of a Rectangle : A = w × h

We are being asked for the Area.

A = w × h = 12 × 5 = 60 m 2

The area is 60 square meters .

Now let's try the example from the top of the page:

Example: Sam and Alex play Tennis. On the weekend Sam played 4 more games than Alex did, and together they played 12 games. How many games did Alex play?

• Use S for how many games Sam played
• Use A for how many games Alex played

We know that Sam played 4 more games than Alex, so: S = A + 4

And we know that together they played 12 games: S + A = 12

We are being asked for how many games Alex played: A

Which means that Alex played 4 games of tennis.

Check: Sam played 4 more games than Alex, so Sam played 8 games. Together they played 8 + 4 = 12 games. Yes!

A slightly harder example:

Example: Alex and Sam also build tables. Together they make 10 tables in 12 days. Alex working alone can make 10 in 30 days. How long would it take Sam working alone to make 10 tables?

• Use a for Alex's work rate
• Use s for Sam's work rate

12 days of Alex and Sam is 10 tables, so: 12a + 12s = 10

30 days of Alex alone is also 10 tables: 30a = 10

We are being asked how long it would take Sam to make 10 tables.

30a = 10 , so Alex's rate (tables per day) is: a = 10/30 = 1/3

Which means that Sam's rate is half a table a day (faster than Alex!)

So 10 tables would take Sam just 20 days.

Should Sam be paid more I wonder?

And another "substitution" example:

Example: Jenna is training hard to qualify for the National Games. She has a regular weekly routine, training for five hours a day on some days and 3 hours a day on the other days. She trains altogether 27 hours in a seven day week. On how many days does she train for five hours?

• The number of "5 hour" days: d
• The number of "3 hour" days: e

We know there are seven days in the week, so: d + e = 7

And she trains 27 hours in a week, with d 5 hour days and e 3 hour days: 5d + 3e = 27

We are being asked for how many days she trains for 5 hours: d

The number of "5 hour" days is 3

Check : She trains for 5 hours on 3 days a week, so she must train for 3 hours a day on the other 4 days of the week.

3 × 5 hours = 15 hours, plus 4 × 3 hours = 12 hours gives a total of 27 hours

Some examples from Geometry:

Example: A circle has an area of 12 mm 2 , what is its radius?

• Use A for Area: A = 12 mm 2
• Use r for radius

And the formula for Area is: A = π r 2

We are being asked for the radius.

We need to rearrange the formula to find the area

Example: A cube has a volume of 125 mm 3 , what is its surface area?

Make a quick sketch:

• Use V for Volume
• Use A for Area
• Use s for side length of cube
• Volume of a cube: V = s 3
• Surface area of a cube: A = 6s 2

We are being asked for the surface area.

First work out s using the volume formula:

Now we can calculate surface area:

An example about Money:

Example: Joel works at the local pizza parlor. When he works overtime he earns 1¼ times the normal rate. One week Joel worked for 40 hours at the normal rate of pay and also worked 12 hours overtime. If Joel earned $660 altogether in that week, what is his normal rate of pay?

• Joel's normal rate of pay: $N per hour
• Joel works for 40 hours at $N per hour = $40N
• When Joel does overtime he earns 1¼ times the normal rate = $1.25N per hour
• Joel works for 12 hours at $1.25N per hour = $(12 × 1¼N) = $15N
• And together he earned $660, so:

$40N + $(12 × 1¼N) = $660

We are being asked for Joel's normal rate of pay $N.

So Joel’s normal rate of pay is $12 per hour

Joel’s normal rate of pay is $12 per hour, so his overtime rate is 1¼ × $12 per hour = $15 per hour. So his normal pay of 40 × $12 = $480, plus his overtime pay of 12 × $15 = $180 gives us a total of $660

More about Money, with these two examples involving Compound Interest

Example: Alex puts $2000 in the bank at an annual compound interest of 11%. How much will it be worth in 3 years?

This is the compound interest formula:

So we will use these letters:

• Present Value PV = $2,000
• Interest Rate (as a decimal): r = 0.11
• Number of Periods: n = 3
• Future Value (the value we want): FV

We are being asked for the Future Value: FV

Example: Roger deposited $1,000 into a savings account. The money earned interest compounded annually at the same rate. After nine years Roger's deposit has grown to $1,551.33 What was the annual rate of interest for the savings account?

The compound interest formula:

• Present Value PV = $1,000
• Interest Rate (the value we want): r
• Number of Periods: n = 9
• Future Value: FV = $1,551.33

We are being asked for the Interest Rate: r

So the annual rate of interest is 5%

Check : $1,000 × (1.05) 9 = $1,000 × 1.55133 = $1,551.33

And an example of a Ratio question:

Example: At the start of the year the ratio of boys to girls in a class is 2 : 1 But now, half a year later, four boys have left the class and there are two new girls. The ratio of boys to girls is now 4 : 3 How many students are there altogether now?

• Number of boys now: b
• Number of girls now: g

The current ratio is 4 : 3

Which can be rearranged to 3b = 4g

At the start of the year there was (b + 4) boys and (g − 2) girls, and the ratio was 2 : 1

b + 4 g − 2 = 2 1

Which can be rearranged to b + 4 = 2(g − 2)

We are being asked for how many students there are altogether now: b + g

There are 12 girls !

And 3b = 4g , so b = 4g/3 = 4 × 12 / 3 = 16 , so there are 16 boys

So there are now 12 girls and 16 boys in the class, making 28 students altogether .

There are now 16 boys and 12 girls, so the ratio of boys to girls is 16 : 12 = 4 : 3 At the start of the year there were 20 boys and 10 girls, so the ratio was 20 : 10 = 2 : 1

And now for some Quadratic Equations :

Example: The product of two consecutive even integers is 168. What are the integers?

Consecutive means one after the other. And they are even , so they could be 2 and 4, or 4 and 6, etc.

We will call the smaller integer n , and so the larger integer must be n+2

And we are told the product (what we get after multiplying) is 168, so we know:

n(n + 2) = 168

We are being asked for the integers

That is a Quadratic Equation , and there are many ways to solve it. Using the Quadratic Equation Solver we get −14 and 12.

Check −14: −14(−14 + 2) = (−14)×(−12) = 168 YES

Check 12: 12(12 + 2) = 12×14 = 168 YES

So there are two solutions: −14 and −12 is one, 12 and 14 is the other.

Note: we could have also tried "guess and check":

• We could try, say, n=10: 10(12) = 120 NO (too small)
• Next we could try n=12: 12(14) = 168 YES

But unless we remember that multiplying two negatives make a positive we might overlook the other solution of (−14)×(−12).

Example: You are an Architect. Your client wants a room twice as long as it is wide. They also want a 3m wide veranda along the long side. Your client has 56 square meters of beautiful marble tiles to cover the whole area. What should the length of the room be?

Let's first make a sketch so we get things right!:

• the length of the room: L
• the width of the room: W
• the total Area including veranda: A
• the width of the room is half its length: W = ½L
• the total area is the (room width + 3) times the length: A = (W+3) × L = 56

We are being asked for the length of the room: L

This is a quadratic equation , there are many ways to solve it, this time let's use factoring :

And so L = 8 or −14

There are two solutions to the quadratic equation, but only one of them is possible since the length of the room cannot be negative!

So the length of the room is 8 m

L = 8, so W = ½L = 4

So the area of the rectangle = (W+3) × L = 7 × 8 = 56

There we are ...

... I hope these examples will help you get the idea of how to handle word questions. Now how about some practice?

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How to Solve Math Problems

Last Updated: April 15, 2024 Fact Checked

This article was co-authored by Daron Cam . Daron Cam is an Academic Tutor and the Founder of Bay Area Tutors, Inc., a San Francisco Bay Area-based tutoring service that provides tutoring in mathematics, science, and overall academic confidence building. Daron has over eight years of teaching math in classrooms and over nine years of one-on-one tutoring experience. He teaches all levels of math including calculus, pre-algebra, algebra I, geometry, and SAT/ACT math prep. Daron holds a BA from the University of California, Berkeley and a math teaching credential from St. Mary's College. This article has been fact-checked, ensuring the accuracy of any cited facts and confirming the authority of its sources. This article has been viewed 593,581 times.

Although math problems may be solved in different ways, there is a general method of visualizing, approaching and solving math problems that may help you to solve even the most difficult problem. Using these strategies can also help you to improve your math skills overall. Keep reading to learn about some of these math problem solving strategies.

Understanding the Problem

• Draw a Venn diagram. A Venn diagram shows the relationships among the numbers in your problem. Venn diagrams can be especially helpful with word problems.
• Draw a graph or chart.
• Arrange the components of the problem on a line.
• Draw simple shapes to represent more complex features of the problem.

Developing a Plan

Solving the Problem

Joseph Meyer

When doing practice problems, promptly check to see if your answers are correct. Use worksheets that provide answer keys for instant feedback. Discuss answers with a classmate or find explanations online. Immediate feedback will help you correct your mistakes, avoid bad habits, and advance your learning more quickly.

Expert Q&A

• Seek help from your teacher or a math tutor if you get stuck or if you have tried multiple strategies without success. Your teacher or a math tutor may be able to easily identify what is wrong and help you to understand how to correct it. Thanks Helpful 0 Not Helpful 0
• Keep practicing sums and diagrams. Go through the concept your class notes regularly. Write down your understanding of the methods and utilize it. Thanks Helpful 0 Not Helpful 0

You Might Also Like

• ↑ Daron Cam. Math Tutor. Expert Interview. 29 May 2020.
• ↑ http://www.interventioncentral.org/academic-interventions/math/math-problem-solving-combining-cognitive-metacognitive-strategies
• ↑ http://tutorial.math.lamar.edu/Extras/StudyMath/ProblemSolving.aspx
• ↑ https://math.berkeley.edu/~gmelvin/polya.pdf

About This Article

To solve a math problem, try rewriting the problem in your own words so it's easier to solve. You can also make a drawing of the problem to help you figure out what it's asking you to do. If you're still completely stuck, try solving a different problem that's similar but easier and then use the same steps to solve the harder problem. Even if you can't figure out how to solve it, try to make an educated guess instead of leaving the question blank. To learn how to come up with a solid plan to use to help you solve a math problem, scroll down! Did this summary help you? Yes No

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Look at this table: x y 1–2 2–4 3–8 4–16 5–32 Write a linear (y=mx+b),...

Part a: Assume that the height of your cylinder is 8 inches. Think of A...

The graph of a function f is shown. Which graph is an antiderivative of f?

A rectangle has area 16m2 . Express the perimeter of the rectangle as a function...

Find the equation of the quadratic function f whose graph is shown below. (5, −2)

Use the discriminant, b2−4ac, to determine the number of solutions of the following quadratic equation....

How many solutions does the equation ||2x-3|-m|=m have if m>0?

If a system of linear equations has infinitely many solutions, then the system is called...

A bacteria population is growing exponentially with a growth factor of 16 each hour.By what...

A system of linear equations with more equations than unknowns is sometimes called an overdetermined...

Express the distance between the numbers 2 and 17 using absolute value. Then find the...

Find the Laplace transform of f(t)=(sin⁡t–cos⁡t)2

Express the interval in terms of an inequality involving absolute value. (0,4)

A function is a ratio of quadratic functions and has a vertical asymptote x =4...

how do you graph y > -2

Find the weighted average of a data set where 10 has a weight of 5,...

The population of California was 29.76 million in 1990 and 33.87 million in 2000. Assume...

The population of a region is growing exponentially. There were 10 million people in 1980...

Two cables BG and BH are attached to the frame ACD as shown.Knowing that the...

A bird flies in the xy-plane with a position vector given by r→=(αt−βt3)i^+γt2j^, with α=2.4...

A movie stuntman (mass 80.0kg) stands on a window ledge 5.0 mabove the floor. Grabbing...

Solve the following linear congruence, 25x≡15(bmod29)

For the equation, a. Write the value or values of the variable that make a...

Which of the following statements is/are correct about logistic regression? (There may be more than...

Compute 4.659×104−2.14×104. Round the answer appropriately. Express your answer as an integer using the proper...

Find the 52nd term of the arithmetic sequence -24,-7, 10

Find the 97th term of the arithmetic sequence 17, 26, 35,

An equation that expresses a relationship between two or more variables, such as H=910(220−a), is...

The football field is rectangular. a. Write a polynomial that represents the area of the...

The equation 1.5r+15=2.25r represents the number r of movies you must rent to spend the...

While standing on a ladder, you drop a paintbrush. The function represents the height y...

When does data modeling use the idea of a weak entity? Give definitions for the...

Write an equation of the line passing through (-2, 5) and parallel to the line...

Find a polar equation for the curve represented by the given Cartesian equation. y =...

Find c such that fave=f(c)

List five integers that are congruent to 4 modulo 12.

A rectangular package to be sent by a postal service can have a maximum combined...

A juggler throws a bowling pin straight up with an initial speed of 8.20 m/s....

The One-to-One Property of natural logarithms states that if ln x = ln y, then...

Find an equation of a parabola that has curvature 4 at the origin.

Find a parametric representation of the solution set of the linear equation. 3x − 1/2y...

Find the product of the complex number and its conjugate. 2-3i

Find the prime factorization of 10!.

Find a polynomial f(x) of degree 5 that has the following zeros. -3, -7, 5...

True or False. The domain of every rational function is the set of all real...

What would be the most efficient step to suggest to a student attempting to complete...

Write a polynomial, P(x), in factored form given the following requirements. Degree: 4 Leading coefficient...

Give a geometric description of the set of points in space whose coordinates satisfy the...

Use the Cauchy-Riemann equations to show that f(z)=z― is not analytic.

Find the local maximum and minimum values and saddle points of the function. If you...

a) Evaluate the polynomial y=x3−7x2+8x−0.35 at x=1.37 . Use 3-digit arithmetic with chopping. Evaluate the...

The limit represents f'(c) for a function f and a number c. Find f and...

A man 6 feet tall walks at a rate of 5 feet per second away...

Find the Maclaurin series for the function f(x)=cos⁡4x. Use the table of power series for...

Suppose that a population develops according to the logistic equation dPdt=0.05P−0.0005P2 where t is measured...

Find transient terms in this general solution to a differential equation, if there are any...

Find the lengths of the sides of the triangle PQR. Is it a right triangle?...

Use vectors to decide whether the triangle with vertices P(1, -3, -2), Q(2, 0, -4),...

Find a path that traces the circle in the plane y=5 with radius r=2 and...

a. Find an upper bound for the remainder in terms of n.b. Find how many...

Find two unit vectors orthogonal to both j−k and i+j.

Obtain the Differential equations: parabolas with vertex and focus on the x-axis.

The amount of time, in minutes, for an airplane to obtain clearance for take off...

Use the row of numbers shown below to generate 12 random numbers between 01 and...

Here’s an interesting challenge you can give to a friend. Hold a $1 (or larger!)...

A random sample of 1200 U.S. college students was asked, "What is your perception of...

The two intervals (114.4, 115.6) and (114.1, 115.9) are confidence intervals (The same sample data...

How many different 10 letter words (real or imaginary) can be formed from the following...

Assume that σ is unknown, the lower 100(1−α)% confidence bound on μ is: a) μ≤x―+tα,n−1sn...

A simple random sample of 60 items resulted in a sample mean of 80. The...

Decresing the sample size, while holding the confidence level and the variance the same, will...

A privately owned liquor store operates both a drive-n facility and a walk-in facility. On...

Show that the equation represents a sphere, and find its center and radius. x2+y2+z2+8x−6y+2z+17=0

Describe in words the region of R3 represented by the equation(s) or inequality. x=5

Suppose that the height, in inches, of a 25-year-old man is a normal random variable...

Find the value and interest earned if $8906.54 is invested for 9 years at %...

Which of the following statements about the sampling distribution of the sample mean is incorrect?...

The random variable x stands for the number of girls in a family of four...

The product of the ages, in years, of three (3) teenagers os 4590. None of...

A simple random sample size of 100 is selected from a population with p=0.40 What...

Which of the following statistics are unbiased estimators of population parameters? Choose the correct answer...

The probability distribution of the random variable X represents the number of hits a baseball...

Let X be a random variable with probability density function.f(x)={c(1−x2)−1<x<10otherwise(a) What is the value of...

A survey of 4826 randomly selected young adults (aged 19 to 25) asked, "What do...

The monthly worldwide average number of airplane crashes of commercial airlines is 2.2. What is...

Given that z is a standard normal random variable, compute the following probabilities.a.P(z≤−1.0)b.P(z≥−1)c.P(z≥−1.5)d.P(−2.5≤z)e.P(−3<z≤0)

Given a standard normal distribution, find the area under the curve that lies(a) to the...

Chi-square tests are best used for which type of dependent variable? nominal, ordinal ordinal interval...

True or False 1.The goal of descriptive statistics is to simplify, summarize, and organize data....

What is the difference between probability distribution and sampling distribution?

A weather forecaster predicts that the temperature in Antarctica will decrease 8∘F each hour for...

The tallest person who ever lived was approximately 8 feet 11 inches tall. a) Write...

An in-ground pond has the shape of a rectangular prism. The pond has a depth...

The average zinc concentration recovered from a sample of measurements taken in 36 different locations...

Why is it important that a sample be random and representative when conducting hypothesis testing?...

Which of the following is true about the sampling distribution of means? A. Shape of...

Give an example of a commutative ring without zero-divisors that is not an integral domain.

List all zero-divisors in Z20. Can you see relationship between the zero-divisors of Z20 and...

Find the integer a such that a≡−15(mod27) and −26≤a≤0

Explain why the function is discontinuous at the given number a. Sketch the graph of...

Two runners start a race at the same time and finish in a tie. Prove...

Which of the following graphs represent functions that have inverse functions?

find the Laplace transform of f (t). f(t)=tsin⁡3t

Find Laplace transforms of sin⁡h3t cos22t

find the Laplace transform of f (t). f(t)=t2cos⁡2t

The Laplace transform of the product of two functions is the product of the Laplace...

The Laplace transform of u(t−2) is (a) 1s+2 (b) 1s−2 (c) e2ss(d)e−2ss

Find the Laplace Transform of the function f(t)=eat

Explain First Shift Theorem & its properties?

Solve f(t)=etcos⁡t

Find Laplace transform of the given function te−4tsin⁡3t

Reduce to first order and solve:x2y″−5xy′+9y=0 y1=x3

(D3−14D+8)y=0

A thermometer is taken from an inside room to the outside ,where the air temperature...

Find that solution of y′=2(2x−y) which passes through the point (0, 1).

Radium decomposes at a rate proportional to the amount present. In 100 years, 100 mg...

Let A, B, and C be sets. Show that (A−B)−C=(A−C)−(B−C)

Suppose that A is the set of sophomores at your school and B is the...

In how many ways can a 10-question true-false exam be answered? (Assume that no questions...

Is 2∈{2}?

How many elements are in the set { 2,2,2,2 } ?

How many elements are in the set { 0, { { 0 } }?

Draw the Hasse diagram representing the partial ordering {(a, b) | a divides b} on...

Flux through a Cube (Eigure 1) A cube has one corner at the origin and...

A well-insulated rigid tank contains 3 kg of saturated liquid-vapor mixture of water at 200...

A water pump that consumes 2 kW of electric power when operating is claimed to...

A hollow, conducting sphere with an outer radius of 0.250 m and an inner radius...

In a truck-loading station at a post office, a small 0.200-kg package is released from...

The magnetic fieldB→in acertain region is 0.128 ,and its direction is that of the z-axis...

A marble moves along the x-axis. The potential-energy functionis shown in Fig. 1a) At which...

A proton is released in a uniform electric field, and it experiences an electric force...

A potters wheel having a radius of 0.50 m and a moment of inertia of12kg⋅m2is...

Two spherical objects are separated by a distance of 1.80×10−3m. The objects are initially electrically...

An airplane pilot sets a compass course due west and maintainsan airspeed of 220 km/h....

Resolve the force F2 into components acting along the u and v axes and determine...

A conducting sphere of radius 0.01m has a charge of1.0×10−9Cdeposited on it. The magnitude of...

Starting with an initial speed of 5.00 m/s at a height of 0.300 m, a...

In the figure a worker lifts a weightωby pulling down on a rope with a...

A stream of water strikes a stationary turbine bladehorizontally, as the drawing illustrates. The incident...

Until he was in his seventies, Henri LaMothe excited audiences by belly-flopping from a height...

A radar station, located at the origin of xz plane, as shown in the figure...

Two snowcats tow a housing unit to a new location at McMurdo Base, Antarctica, as...

You are on the roof of the physics building, 46.0 m above the ground. Your...

A block is on a frictionless table, on earth. The block accelerates at5.3ms2when a 10...

A 0.450 kg ice puck, moving east with a speed of3.00mshas a head in collision...

A uniform plank of length 2.00 m and mass 30.0 kg is supported by three...

An adventurous archaeologist crosses between two rock cliffs by slowly going hand-over-hand along a rope...

A ski tow operates on a 15.0 degrees slope of lenth 300m. The rope moves...

Two blocks with masses 4.00 kg and 8.00 kg are connected by string and slide...

From her bedroom window a girl drops a water-filled balloon to the ground 6.0 m...

A 730-N man stands in the middle of a frozen pond of radius 5.0 m....

A 5.00 kg package slides 1.50 m down a long ramp that is inclined at12.0∘below...

Ropes 3m and 5m in length are fastened to a holiday decoration that is suspended...

A skier of mass 70 kg is pulled up a slope by a motor driven...

A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid,...

A sled with rider having a combined mass of 120 kg travels over the perfectly...

A 7.00- kg bowling ball moves at 3.00 m/s. How fast must a 2.45- g...

Two point chargesq1=+2.40nC andq2=−6.50nC are 0.100 m apart. Point A is midway between them and...

A block of mass m slides on a horizontal frictionless table with an initial speed...

A space traveler weights 540 N on earth. what will the traveler weigh on another...

A block of mass m=2.20 kg slides down a 30 degree incline which is 3.60...

A weatherman carried an aneroid barometer from the groundfloor to his office atop a tower....

If a negative charge is initially at rest in an electric field, will it move...

A coin with a diameter of 2.40cm is dropped on edge on to a horizontal...

An atomic nucleus initially moving at 420 m/s emits an alpha particle in the direction...

An 80.0-kg skydiver jumps out of a balloon at an altitude of1000 m and opens...

A 0.145 kg baseball pitched at 39.0 m/s is hit on a horizontal line drive...

A 1000 kg safe is 2.0 m above a heavy-duty spring when the rope holding...

A 500 g ball swings in a vertical circle at the end of a1.5-m-long string....

A rifle with a weight of 30 N fires a 5.0 g bullet with a...

The tires of a car make 65 revolutions as the car reduces its speed uniformly...

A 2.0- kg piece of wood slides on the surface. The curved sides are perfectly...

A 292 kg motorcycle is accelerating up along a ramp that is inclined 30.0° above...

A projectile is shot from the edge of a cliff 125 m above ground level...

A lunch tray is being held in one hand, as the drawing illustrates. The mass...

The initial velocity of a car, vi, is 45 km/h in the positivex direction. The...

An Alaskan rescue plane drops a package of emergency rations to a stranded party of...

Raindrops make an angle theta with the vertical when viewed through a moving train window....

A 0.50 kg ball that is tied to the end of a 1.1 m light...

If the coefficient of static friction between your coffeecup and the horizontal dashboard of your...

A car is initially going 50 ft/sec brakes at a constant rate (constant negative acceleration),...

A swimmer is capable of swimming 0.45m/s in still water (a) If sheaim her body...

A block is hung by a string from inside the roof of avan. When the...

A race driver has made a pit stop to refuel. Afterrefueling, he leaves the pit...

A relief airplane is delivering a food package to a group of people stranded on...

The eye of a hurricane passes over Grand Bahama Island. It is moving in a...

An extreme skier, starting from rest, coasts down a mountainthat makes an angle25.0∘with the horizontal....

Four point charges form a square with sides of length d, as shown in the...

In a scene in an action movie, a stuntman jumps from the top of one...

The spring in the figure (a) is compressed by length delta x . It launches...

An airplane propeller is 2.08 m in length (from tip to tip) and has a...

A helicopter carrying dr. evil takes off with a constant upward acceleration of5.0ms2. Secret agent...

A 15.0 kg block is dragged over a rough, horizontal surface by a70.0 N force...

A box is sliding with a speed of 4.50 m/s on a horizontal surface when,...

3.19 Win the Prize. In a carnival booth, you can win a stuffed giraffe if...

A car is stopped at a traffic light. It then travels along a straight road...

a. When the displacement of a mass on a spring is12A, what fraction of the...

At a certain location, wind is blowing steadily at 10 m/s. Determine the mechanical energy...

A jet plane lands with a speed of 100 m/s and can accelerate at a...

In getting ready to slam-dunk the ball, a basketball player starts from rest and sprints...

An antelope moving with constant acceleration covers the distance between two points 70.0 m apart...

A bicycle with 0.80-m-diameter tires is coasting on a level road at 5.6 m/s. A...

The rope and pulley have negligible mass, and the pulley is frictionless. The coefficient of...

A proton with an initial speed of 800,000 m/s is brought to rest by an...

The volume of a cube is increasing at the rate of 1200 cm supmin at...

An airplane starting from airport A flies 300 km east, then 350 km at 30...

To prove: In the following figure, triangles ABC and ADC are congruent. Given: Figure is...

Conduct a formal proof to prove that the diagonals of an isosceles trapezoid are congruent....

The distance between the centers of two circles C1 and C2 is equal to 10...

Segment BC is Tangent to Circle A at Point B. What is the length of...

Find an equation for the surface obtained by rotating the parabola y=x2 about the y-axis.

Find the area of the parallelogram with vertices A(-3, 0), B(-1 , 3), C(5, 2),...

If the atomic radius of lead is 0.175 nm, find the volume of its unit...

At one point in a pipeline the water’s speed is 3.00 m/s and the gauge...

Find the volume of the solid in the first octant bounded by the coordinate planes,...

A paper cup has the shape of a cone with height 10 cm and radius...

A light wave has a 670 nm wavelength in air. Its wavelength in a transparent...

An airplane pilot wishes to fly due west. A wind of 80.0 km/h (about 50...

Find the equation of the sphere centered at (-9, 3, 9) with radius 5. Give...

Determine whether the congruence is true or false. 5≡8 mod 3

Find all whole number solutions of the congruence equation. (2x+1)≡5 mod 4

Determine whether the congruence is true or false. 100≡20 mod 8

I want example of an undefined term and a defined term in geometry and explaining...

Two fair dice are rolled. Let X equal the product of the 2dice. Compute P{X=i}...

Suppose that two defective refrigerators have been included in a shipment of six refrigerators. The...

Based on the Normal model N(100, 16) describing IQ scores, what percent of peoples

The probability density function of the net weight in pounds of a packaged chemical herbicide...

Let X represent the difference between the number of heads and the number of tails...

An urn contains 3 red and 7 black balls. Players A and B withdraw balls...

80% A poll is given, showing are in favor of a new building project. 8...

The probability that the San Jose Sharks will win any given game is 0.3694 based...

Find the value of P(X=7) if X is a binomial random variable with n=8 and...

Find the value of P(X=8) if X is a binomial random variable with n=12 and...

On a 8 question multiple-choice test, where each question has 2 answers, what would be...

If you toss a fair coin 11 times, what is the probability of getting all...

A coffee connoisseur claims that he can distinguish between a cup of instant coffee and...

Two firms V and W consider bidding on a road-building job, which may or may...

Two cards are drawn without replacement from an ordinary deck, find the probability that the...

In August 2012, tropical storm Isaac formed in the Caribbean and was headed for the...

A local bank reviewed its credit card policy with the intention of recalling some of...

The accompanying table gives information on the type of coffee selected by someone purchasing a...

A batch of 500 containers for frozen orange juice contains 5 that are defective. Two...

The probability that an automobile being filled with gasoline also needs an oil change is...

Let the random variable X follow a normal distribution with μ=80 and σ2=100. a. Find...

A card is drawn randomly from a standard 52-card deck. Find the probability of the...

The next number in the series 38, 36, 30, 28, 22 is ?

What is the coefficient of x8y9 in the expansion of (3x+2y)17?

A boat on the ocean is 4 mi from the nearest point on a straight...

How many different ways can you make change for a quarter? (Different arrangements of the...

Seven balls are randomly withdrawn from an urn that contains 12 red, 16 blue, and...

Approximately 80,000 marriages took place in the state of New York last year. Estimate the...

The probability that a student passes the Probability and Statistics exam is 0.7. (i)Find the...

Customers at a gas station pay with a credit card (A), debit card (B), or...

It is conjectured that an impurity exists in 30% of all drinking wells in a...

Assume that the duration of human pregnancies can be described by a Normal model with...

According to a renowned expert, heavy smokers make up 70% of lung cancer patients. If...

Two cards are drawn successively and without replacement from an ordinary deck of playing cards...

Suppose that vehicles taking a particular freeway exit can turn right (R), turn left (L),...

A bag contains 6 red, 4 blue and 8 green marbles. How many marbles of...

A normal distribution has a mean of 50 and a standard deviation of 4. Please...

Seven women and nine men are on the faculty in the mathematics department at a...

An automatic machine in a manufacturing process is operating properly if the lengths of an...

Three cards are drawn without replacement from the 12 face cards (jacks, queens, and kings)...

Among 157 African-American men, the mean systolic blood pressure was 146 mm Hg with a...

A TIRE MANUFACTURER WANTS TO DETERMINE THE INNER DIAMETER OF A CERTAIN GRADE OF TIRE....

Differentiate the three measures of central tendency: ungrouped data.

Find the mean of the following data: 12,10,15,10,16,12,10,15,15,13

A wallet containing four P100 bills, two P200 bills, three P500 bills, and one P1,000...

The number of hours per week that the television is turned on is determined for...

Data was collected for 259 randomly selected 10 minute intervals. For each ten-minute interval, the...

Sixty-five randomly selected car salespersons were asked the number of cars they generally sell in...

A normal distribution has a mean of 80 and a standard deviation of 14. Determine...

True or false: a. All normal distributions are symmetrical b. All normal distributions have a...

Would you expect distributions of these variables to be uniform, unimodal, or bimodal? Symmetric or...

Annual sales, in millions of dollars, for 21 pharmaceutical companies follow. 8408 1374 1872 8879...

The velocity function (in meters per second) is given for a particle moving along a...

Find the area of the parallelogram with vertices A(-3,0) , B(-1,6) , C(8,5) and D(6,-1)

What is the area of the parallelogram with vertices A(-3, 0), B(-1, 5), C(7, 4),...

The integral represents the volume of a solid. Describe the solid. π∫01(y4−y8)dy a) The integral...

Two components of a minicomputer have the following joint pdf for their useful lifetimes X...

Use the table of values of f(x,y) to estimate the values of fx(3,2), fx(3,2.2), and...

Calculate net price factor and net price. Dollars list price −435.20$ Trade discount rate −26%,15%,5%.

Represent the line segment from P to Q by a vector-valued function and by a...

(x2+2xy−4y2)dx−(x2−8xy−4y2)dy=0

If f is continuous and integral 0 to 9 f(x)dx=4, find integral 0 to 3...

Find the parametric equation of the line through a parallel to ba=[3−4],b=[−78]

Find the velocity and position vectors of a particle that has the given acceleration and...

If we know that the f is continuous and integral 0 to 4f(x)dx=10, compute the...

Integration of (y⋅tan⁡xy)

For the matrix A below, find a nonzero vector in the null space of A...

Find a nonzero vector orthogonal to the plane through the points P, Q, and R....

Suppose that the augmented matrix for a system of linear equations has been reduced by...

Find two unit vectors orthogonal to both (3 , 2, 1) and (- 1, 1,...

What is the area of the parallelogram whose vertices are listed? (0,0), (5,2), (6,4), (11,6)

Using T defined by T(x)=Ax, find a vector x whose image under T is b,...

Use the definition of Ax to write the matrix equation as a vector equation, or...

We need to find the volume of the parallelepiped with only one vertex at the...

List five vectors in Span {v1,v2}. For each vector, show the weights on v1 and...

(1) find the projection of u onto v and (2) find the vector component of...

Find the area of the parallelogram determined by the given vectors u and v. u...

(a) Find the point at which the given lines intersect. r = 2,...

(a) find the transition matrix from B toB′,(b) find the transition matrix fromB′to B,(c) verify...

A box contains 5 red and 5 blue marbles. Two marbles are withdrawn randomly. If...

Given the following vector X, find anon zero square marix A such that AX=0; You...

Construct a matrix whose column space contains (1, 1, 5) and (0, 3.1) and whose...

At what point on the paraboloid y=x2+z2 is the tangent plane parallel to the plane...

Label the following statements as being true or false. (a) If V is a vector...

Find the Euclidean distance between u and v and the cosine of the angle between...

Write an equation of the line that passes through (3, 1) and (0, 10)

There are 100 two-bedroom apartments in the apartment building Lynbrook West.. The montly profit (in...

State and prove the linearity property of the Laplace transform by using the definition of...

The analysis of shafts for a compressor is summarized by conformance to specifications. Suppose that...

The Munchies Cereal Company combines a number of components to create a cereal. Oats and...

Movement of a Pendulum A pendulum swings through an angle of 20∘ each second. If...

If sin⁡x+sin⁡y=aandcos⁡x+cos⁡y=b then find tan⁡(x−y2)

Find the values of x such that the angle between the vectors (2, 1, -1),...

Find the dimensions of the isosceles triangle of largest area that can be inscribed in...

Suppose that you are headed toward a plateau 50 meters high. If the angle of...

Airline passengers arrive randomly and independently at the passenger-screening facility at a major international airport....

Find an equation of the plane. The plane through the points (2, 1, 2), (3,...

Match each of the trigonometric expressions below with the equivalent non-trigonometric function from the following...

two small spheres spaced 20.0cm apart have equal charges. How many extra electrons must be...

The base of a pyramid covers an area of 13.0 acres (1 acre =43,560 ft2)...

Find out these functions' domain and range. To find the domain in each scenario, identify...

Your bank account pays an interest rate of 8 percent. You are considering buying a...

Whether f is a function from Z to R ifa)f(n)=±n.b)f(n)=n2+1.c)f(n)=1n2−4.

The probability density function of X, the lifetime of a certain type of electronic device...

A sandbag is released by a balloon that is rising vertically at a speed of...

A proton is located in a uniform electric field of2.75×103NCFind:a) the magnitude of the electric...

A rectangular plot of farmland are finite on one facet by a watercourse and on...

A solenoid is designed to produce a magnetic field of 0.0270 T at its center....

I want to find the volume of the solid enclosed by the paraboloidz=2+x2+(y−2)2and the planesz=1,x=−1y=0,andy=4

Let W be the subspace spanned by the u’s, and write y as the sum...

Can u find the point on the planex+2y+3z=13that is closest to the point (1,1,1). You...

A spring of negligible mass stretches 3.00 cm from its relaxed length when a force...

A force of 250 Newtons is applied to a hydraulic jack piston that is 0.01...

Three identical blocks connected by ideal strings are being pulled along a horizontal frictionless surface...

A credit card contains 16 digits between 0 and 9. However, only 100 million numbers...

Every real number is also a complex number? True of false?

Let F be a fixed 3x2 matrix, and let H be the set of all...

Find a vector a with representation given by the directed line segment AB. Draw AB...

Find A such that the given set is Col A. {[2s+3tr+s−2t4r+s3r−s−t]:r,s,t real}

Find the vector that has the same direction as (6, 2, -3) but is four...

For the matrices (a) find k such that Nul A is a subspace of Rk,...

How many subsets with an odd number of elements does a set with 10 elements...

In how many ways can a set of five letters be selected from the English...

Suppose that f(x) = x/8 for 3 < x < 5. Determine the following probabilities:...

Describe all solutions of Ax=0 in parametric vector form, where A is row equivalent to...

Find two vectors parallel to v of the given length. v=PQ→ with P(1,7,1) and Q(0,2,5);...

A dog in an open field runs 12.0 m east and then 28.0 m in...

Can two events with nonzero probabilities be both independent and mutually exclusive? Explain your reasoning.

Use the Intermediate Value Theorem to show that there is a root of the given...

In a fuel economy study, each of 3 race cars is tested using 5 different...

A company has 34 salespeople. A board member at the company asks for a list...

A dresser drawer contains one pair of socks with each of the following colors: blue,...

A restaurant offers a $12 dinner special with seven appetizer options, 12 choices for an...

A professor writes 40 discrete mathematics true/false questions. Of the statements in these questions, 17...

Suppose E(X)=5 and E[X(X–1)]=27.5, find ∈(x2) and the variance.

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25 Fun Maths Problems For KS2 And KS3 (From Easy To Very Hard!)

Fun maths problems are one of the things mathematicians love about the subject; they provide an opportunity to apply mathematical knowledge, logic and problem solving skills all at once.  In this article, we’ve compiled 25 fun maths problems, each covering various topics and question types. They’re aimed at students in KS2 & KS3. We’ve categorised them as:

Maths word problems

Maths puzzles, fraction problems, multiplication and division problems, geometry problems, problem solving questions, maths puzzles are everywhere, how should teachers use these maths problems.

Teachers could make use of these maths problem solving questions in a number of ways, such as:

• embed into a relevant maths topic’s teaching.
• settling tasks at the beginning of lessons.
• break up or extend a maths worksheet.
• keep students thinking mathematically after the main lesson has finished.

Some are based on real life or historical maths problems, and some include ‘bonus’ maths questions to help to extend the problem solving fun! As you read through these problems, think about how you could adjust them to be relevant to your students or to practise different skills. 

These maths problems can also be used as introductory puzzles for maths games such as those introduced at the following links:

• KS2 maths games
• KS3 maths games

Need more support teaching reasoning, problem solving and planning for depth ? Read here for free CPD for you and your team of teachers.

1. Home on time – easy

Type: Time, Number, Addition

A cinema screening starts at 14:35. The movie lasts for 2 hours, 32 minutes after 23 minutes of adverts. It took 20 minutes to get to the cinema. What time should you tell your family that you’ll be home?

Answer: 17:50

2. A nugget of truth – mixed

Type: Times Tables, Multiplication, Multiples, Factors, Problem Solving 

Chicken nuggets come in boxes of 6, 9 or 20, so you can’t order 7 chicken nuggets. How many other impossible quantities can you find (not including fractions or decimals)?

Answer: 1, 2, 3, 4, 5, 7, 8, 10, 11, 13, 14, 16, 17, 19, 22, 23, 25, 28, 31, 34, 37, or 43

There is actually a theorem which can be used to prove that every integer quantity greater than 43 can be ordered.

3. A pet problem – mixed

Type: Number, Problem Solving, Forming and Solving Equations, Simultaneous Equations, Algebra

Eight of my pets aren’t dogs, five aren’t rabbits, and seven aren’t cats. How many pets do I have?

Answer: 10 pets (5 rabbits, 3 cats, 2 dogs)

4. The price of things – mixed

Type: lateral thinking problem

A mouse costs £10, a bee costs £15, and a spider costs £20. How much does a duck cost? Answer: £5 (£2.50 per leg)

Looking for more word problems, solutions and explanations? Read our article on word problems for primary school.

25 Fun Maths Problems - Printable

Download a printable version of these fun maths problems together with answers and mark scheme.

5. A dicey maths challenge – easy

Type: Place value, number, addition, problem solving

Roll three dice to generate three place value digits. What’s the biggest number you can make out of these digits? What’s the smallest number you can make?

Add these two numbers together. What do you get?

Answer: In most cases, 1,089.

Bonus: Who got a different result? Why?

6. PIN problem solving – mixed

Type: Logic, problem solving, reasoning

I’ve forgotten my PIN. Six incorrect attempts locks my account: I’ve used five! Two digits are displayed after each unsuccessful attempt: “2, 0” means 2 digits from that guess are in the PIN, but 0 are in the right place.

What should my sixth attempt be?

Answer: 6347

7. So many birds – mixed

Type: Triangular Numbers, Sequences, Number, Problem Solving

On the first day of Christmas my true love gave me one gift. On the second day they gave me another pair of gifts plus a copy of what they gave me on day one. On day 3, they gave me three new gifts, plus another copy of everything they’d already given me. If they keep this up, how many gifts will I have after twelve days?

Answer: 364

Bonus: This could be calculated as 1 + (1 + 2) + (1 + 2 + 3) + … but is there an easier way? What percentage of my gifts do I receive on each day?

8. I 8 sum maths questions – mixed

Type: Number, Place Value, Addition, Problem Solving, Reasoning

Using only addition and the digit 8, can you make 1,000? You can put 8s together to make 88, for example.

Answer: 888 + 88 + 8 + 8 + 8 = 1,000 Bonus: Which other digits allow you to get 1,000 in this way?

9. Quizzical – easy

Type: Fractions, Adding Fractions, Equivalent Fractions, Fractions to Percentages

4 friends entered a maths quiz. One answered \frac{1}{5} of the maths questions, one answered \frac{1}{10} , one answered \frac{1}{4} , and the other answered \frac{4}{25} . What percentage of the questions did they answer altogether?

Answer: 71%

10. Ancient problem solving – mixed

Type: Fractions, Reasoning, Problem Solving

Ancient Egyptians only used unit fractions (like \frac{1}{2} , \frac{1}{3} or \frac{1}{4} ). For \frac{2}{3} , they’d write \frac{1}{3} + \frac{1}{3} . How might they write \frac{5}{8} ?

Answer: \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} + \frac{1}{8} is correct. So is \frac{1}{2} + \frac{1}{8} .

Bonus: Which solution is better? Why? Can you find any more? What if subtractions are allowed?

Learn more about unit fractions here

11. everybody wants a pizza the action – hard.

An infinite number of mathematicians buy pizza. The first wants \frac{1}{2} pizza. The second wants \frac{1}{4} pizza. The third & fourth want \frac{1}{8} and \frac{1}{16} each, and so on. How many pizzas should they order?

Answer: 1 Each successive mathematician wants a slice that is exactly half of what is left:

12. Shade it black – hard

Type: Fractions, Reasoning, Problem Solving What fraction of this image is shaded black?

Answer: \frac{1}{3}

Look at the L-shaped part made up of two white and one black squares: \frac{1}{3} of this part is shaded. Zoom in on the top-right quarter of the image, which looks exactly the same as the whole image, and use the same reasoning to find what fraction of its L-shaped portion is shaded. Imagine zooming in to do the same thing again and again…

13. Giving is receiving – easy

Type: Number, Reasoning, Problem Solving

5 people give each other a present. How many presents are given altogether?

14. Sharing is caring – mixed

I have 20 sweets. If I share them equally with my friends, there are 2 left over. If one more person joins us, there are 6 sweets left. How many friends am I with?

Answer: 6 people altogether (so 5 friends!)

15. Times tables secrets – mixed

Type: Area, 2D Shape, Rectangles

Here are 77 letters:

BYHRCGNGNEOEAAHGHGCURPUTSTSASHHSBOBOREOPEEMEMEELATPEPEFADPHLTLTUT IEEOHOHLENRYTITIIAGBMTNTNFCGEIIGIG

How many different rectangular grids could you arrange all 77 letters into?

Answer: Four: 1⨉77, 77⨉1, 11⨉7 & 7⨉11. If the letters are arranged into one of these, a message appears, reading down each column starting from the top left.

Bonus: Can you find any more integers with the same number of factors as 77? What do you notice about these factors (think about prime numbers)? Can you use this system to hide your own messages?

16. Laugh it up – hard

Type: Multiples, Lowest Common Multiple, Times Tables, Division, Time

One friend jumps every \frac{1}{3} of a minute. Another jumps every 31 seconds. When will they jump together? Answer: After 620 seconds

17. Pictures of matchstick triangles – easy

Type: 2D Shapes, Equilateral Triangles, Problem Solving, Reasoning

Look at the matchsticks arranged below. How many equilateral triangles are there?

Answer: 13 (9 small, 3 medium, 1 large)

Bonus: What if the biggest triangle only had two matchsticks on each side? What if it had four?

18. Dissecting squares – mixed

Type: Reasoning, Problem Solving

What’s the smallest number of straight lines you could draw on this grid such that each square has a line going through it?

19. Make it right – mixed

Type: Pythagoras’ theorem

This triangle does not agree with Pythagoras’ theorem. 

Adding, subtracting, multiplying or dividing each of the side lengths by the same integer can fix it. What is the integer?

Answer: 3 

8 – 3 = 5

The new side lengths are 3, 4 and 5 and  32 + 42 = 52.

20. A most regular maths question – hard

Type: Polygons, 2D Shapes, tessellation, reasoning, problem-solving, patterns

What is the regular polygon with the largest number of sides that will self-tessellate?

Answer: Hexagon.

Regular polygons tessellate if one interior angle is a factor of 360°. The interior angle of a hexagon is 120°. This is the largest factor less than 180°.

21. Pleased to meet you – easy

Type: Number Problem, Reasoning, Problem-Solving

5 people meet; each shakes everyone else’s hand once. How many handshakes take place?

Person A shakes 4 people’s hands. Person B has already shaken Person A’s hand, so only needs to shake 3 more, and so on.

Bonus: How many handshakes would there be if you did this with your class?

22. All relative – easy

Type: Number, Reasoning, Problem-Solving

When I was twelve my brother was half my age. I’m 40 now, so how old is he?

23. It’s about time – mixed

Type: Time, Reasoning, Problem-Solving

When is “8 + 10 = 6” true?

Answer: When you’re telling the time (8am + 10 hours = 6pm)

24. More than a match – mixed

Type: Reasoning, Problem-Solving, Roman Numerals, Numerical Notation

Here are three matches:

How can you add two more matches, but get eight? Answer: Put the extra two matches in a V shape to make 8 in Roman Numerals:

25. Leonhard’s graph – hard

Type: Reasoning, Problem-Solving, Logic

Leonhard’s town has seven bridges as shown below. Can you find a route around the town that crosses every bridge exactly once?

Answer: No!

This is a classic real life historical maths problem solved by mathematician Leonhard Euler (rhymes with “boiler”). The city was Konigsberg in Prussia (now Kaliningrad, Russia). Not being able to find a solution is different to proving that there aren’t any! Euler managed to do this in 1736, practically inventing graph theory in the process.

Many of these 25 maths problems are rooted in real life, from everyday occurrences to historical events. Others are just questions that might arise if you say “what if…?”. The point is that although there are many lists of such problem solving maths questions that you can make use of, with a little bit of experience and inspiration you could create your own on almost any topic – and so could your students. 

For a kick-starter on creating your own maths problems, read our article on KS3 maths problem solving .

Looking for additional support and resources at KS3? You are welcome to download any of the secondary maths resources from Third Space Learning’s resource library for free. There is a section devoted to GCSE maths revision with plenty of maths worksheets and GCSE maths questions . There are also maths tests for KS3, including a Year 7 maths test , a Year 8 maths test and a Year 9 maths test For children who need more support, our maths intervention programmes for KS3 achieve outstanding results through a personalised one to one tuition approach.

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30 Fun Maths Questions with Answers

Table of Contents

Introduction

Mathematics can be fun if you treat it the right way. Maths is nothing less than a game, a game that polishes your intelligence and boosts your concentration. Compared to older times, people have a better and friendly approach to mathematics which makes it more appealing. The golden rule is to know that maths is a mindful activity rather than a task.

There is nothing like hard math problems or tricky maths questions, it’s just that you haven’t explored mathematics well enough to comprehend its easiness and relatability. Maths tricky questions and answers can be transformed into fun math problems if you look at it as if it is a brainstorming session. With the right attitude and friends and teachers, doing math can be most entertaining and delightful.

Math is interesting because a few equations and diagrams can communicate volumes of information. Treat math as a language, while moving to rigorous proof and using logical reason for performing a particular step in a proof or derivation.

Treating maths as a language totally eradicates the concept of hard math problems or tricky maths questions from your mind. Introducing children to fun maths questions can create a strong love and appreciation for maths at an early age. This way you are setting up the child’s successful future. Fun math problems will urge your child to choose to solve it over playing bingo or baking.

Apparently, there are innumerable methods to make easy maths tricky questions and answers. This includes the inception of the ideology that maths is simpler than their fear. This can be done by connecting maths with everyday life. Practising maths with the aid of dice, cards, puzzles and tables reassures that your child effectively approaches Maths.

If you wish to add some fun and excitement into educational activities, also check out

• Check out some mind-blowing Math Magic Tricks!
• Mental Maths: How to Improve it?

Cuemath is one of the world's leading math learning platforms that offers LIVE 1-to-1 online math classes for grades K-12 . Our mission is to transform the way children learn math, to help them excel in school and competitive exams. Our expert tutors conduct 2 or more live classes per week, at a pace that matches the child's learning needs.

Fun Maths Questions with answers - PDF

Here is the Downloadable PDF that consists of Fun Math questions. Click the Download button to view them.

Here are some fun, tricky and hard to solve maths problems that will challenge your thinking ability.

Answer: is 3, because ‘six’ has three letters

What is the number of parking space covered by the car?

This tricky math problem went viral a few years back after it appeared on an entrance exam in Hong Kong… for six-year-olds. Supposedly the students had just 20 seconds to solve the problem!

Believe it or not, this “math” question actually requires no math whatsoever. If you flip the image upside down, you’ll see that what you’re dealing with is a simple number sequence.

Replace the question mark in the above problem with the appropriate number.

Which number is equivalent to 3^(4)÷3^(2)

This problem comes straight from a standardized test given in New York in 2014.

There are 49 dogs signed up for a dog show. There are 36 more small dogs than large dogs. How many small dogs have signed up to compete? 

This question comes directly from a second grader's math homework.

To figure out how many small dogs are competing, you have to subtract 36 from 49 and then divide that answer, 13 by 2, to get 6.5 dogs, or the number of big dogs competing. But you’re not done yet! You then have to add 6.5 to 36 to get the number of small dogs competing, which is 42.5. Of course, it’s not actually possible for half a dog to compete in a dog show, but for the sake of this math problem let’s assume that it is.

Add 8.563 and 4.8292.

Adding two decimals together is easier than it looks. Don’t let the fact that 8.563 has fewer numbers than 4.8292 trip you up. All you have to do is add a 0 to the end of 8.563 and then add like you normally would.

I am an odd number. Take away one letter and I become even. What number am I?

Answer:  Seven (take away the ‘s’ and it becomes ‘even’).

Using only an addition, how do you add eight 8’s and get the number 1000?

Answer: 

888 + 88 + 8 + 8 + 8 = 1000

Sally is 54 years old and her mother is 80, how many years ago was Sally’s mother times her age?

41 years ago, when Sally was 13 and her mother was 39.

Which 3 numbers have the same answer whether they’re added or multiplied together?

There is a basket containing 5 apples, how do you divide the apples among 5 children so that each child has 1 apple while 1 apple remains in the basket?

4 children get 1 apple each while the fifth child gets the basket with the remaining apple still in it.

There is a three-digit number. The second digit is four times as big as the third digit, while the first digit is three less than the second digit. What is the number?

Fill in the question mark

Two girls were born to the same mother, at the same time, on the same day, in the same month and the same year and yet somehow they’re not twins. Why not?

Because there was a third girl, which makes them triplets!

A ship anchored in a port has a ladder which hangs over the side. The length of the ladder is 200cm, the distance between each rung in 20cm and the bottom rung touches the water. The tide rises at a rate of 10cm an hour. When will the water reach the fifth rung?

The tide raises both the water and the boat so the water will never reach the fifth rung. 

The day before yesterday I was 25. The next year I will be 28. This is true only one day in a year. What day is my Birthday?  

You have a 3-litre bottle and a 5-litre bottle. How can you measure 4 litres of water by using 3L and 5L bottles? 

Solution 1 :

First, fill 3Lt bottle and pour 3 litres into 5Lt bottle.

Again fill the 3Lt bottle. Now pour 2 litres into the 5Lt bottle until it becomes full.

Now empty 5Lt bottle.

Pour remaining 1 litre in 3Lt bottle into 5Lt bottle.

Now again fill 3Lt bottle and pour 3 litres into 5Lt bottle.

Now you have 4 litres in the 5Lt bottle. That’s it.

Solution 2 :

First, fill the 5Lt bottle and pour 3 litres into 3Lt bottle.

Empty 3Lt bottle.

Pour remaining 2 litres in  5Lt bottle into 3Lt bottle.

Again fill the 5Lt bottle and pour 1 litre into 3 Lt bottle until it becomes full.

3 Friends went to a shop and purchased 3 toys. Each person paid Rs.10 which is the cost of one toy. So, they paid Rs.30 i.e. total amount. The shop owner gave a discount of Rs.5 on the total purchase of 3 toys for Rs.30. Then, among Rs.5, Each person has taken Rs.1 and remaining Rs.2 given to the beggar beside the shop. Now, the effective amount paid by each person is Rs.9 and the amount given to the beggar is Rs.2. So, the total effective amount paid is 9*3 = 27 and the amount given to beggar is Rs.2, thus the total is Rs.29. Where has the other Rs.1 gone from the original Rs.30?

The logic is payments should be equal to receipts. We cannot add the amount paid by persons and the amount given to the beggar and compare it to Rs.30.The total amount paid is ₹27. So, from ₹27, the shop owner received 25 rupees and beggar received ₹ 2. Thus, payments are equal to receipts.

How to get a number 100 by using four sevens (7’s) and a one (1)?

Answer 1:   177 – 77 = 100 ;

Answer 2: (7+7) * (7 + (1/7)) = 100 

Move any four matches to get 3 equilateral triangles only (don’t remove matches)

Find the area of the red triangle.

To solve this fun maths question, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, then adding 79 and 10 and subsequently subtracting 72 and 8 to get 9 should make sense.

 How many feet are in a mile? 

Solve  - 15+ (-5x) =0

What is 1.92÷3

A man is climbing up a mountain which is inclined. He has to travel 100 km to reach the top of the mountain. Every day He climbs up 2 km forward in the day time. Exhausted, he then takes rest there at night time. At night, while he is asleep, he slips down 1 km backwards because the mountain is inclined. Then how many days does it take him to reach the mountain top? 

 If 72 x 96 = 6927, 58 x 87 = 7885, then 79 x 86 = ?

Answer:  

Look at this series: 36, 34, 30, 28, 24, … What number should come next?

  Look at this series: 22, 21, 23, 22, 24, 23, … What number should come next?

If 13 x 12 = 651 & 41 x 23 = 448, then, 24 x 22 =?

Look at this series: 53, 53, 40, 40, 27, 27, … What number should come next?

The ultimate goals of mathematics instruction are students understanding the material presented, applying the skills, and recalling the concepts in the future. There's little benefit in students recalling a formula or procedure to prepare for an assessment tomorrow only to forget the core concept by next week.

Teachers must focus on making sure that the students understand the material and not just memorize the procedures. After you learn the answers to a fun maths question, you begin to ask yourself how you could have missed something so easy. The truth is, most trick questions are designed to trick your mind, which is why the answers to fun maths questions are logical and easy. 

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Maths Quiz Questions

We are providing here maths quiz questions for children to help them increase their knowledge of the subject. These questions are prepared based on fundamental mathematical concepts. The problems here are provided with four multiple answers and students have to choose the right answer. The questions here could be solved by students of all the classes from 6 to 10, as they are based on basic arithmetic operations and geometrical concepts. Thus, on solving them they can also participate in quiz competitions conducted in schools.

Solving these quizzes will help students to gain more knowledge and boost their problem-solving skills. These questions are very easy to solve and will not take much time. Hence, it is recommended to all the children to solve each one of them and test their abilities.

Maths Quiz Questions with Answers (MCQs)

Let us answer here some of the quizzes which are based on simple arithmetic concepts. These problems are based on fundamental concepts, which students can easily answer without picking up a pen and paper.

Q.1. What is the sum of 130+125+191?

Q.2: If we minus 712 from 1500, how much do we get?

Q.3: 50 times of 8 is equal to:

Q.4: 110 divided by 10 is:

D. None of these

Q.5: 20+(90÷2) is equal to:

Q.6: The product of 82 and 5 is:

Q.7: Find the missing terms in multiple of 3: 3, 6, 9, __, 15

Q.8: Solve 24÷8+2.

Q.9: Solve: 300 – (150×2)

Q.10: The product of 121 x 0 x 200 x 25 is

Q.11: What is the next prime number after 5?

Also, read:

• Class 8 Maths MCQs
• Class 9 Maths MCQs
• Class 10 Maths MCQs

Maths Quizzes and Answers

Here are some quiz questions which children should be able to answer quickly.

Q.12: The circumference of the circle is also sometimes called:

Answer: Perimeter of a circle

Q.13: 90 – 35 is equal to:

Q.14: 72 divided by 8 is equal to:

Q.15: How many sides does a decagon have?

Answer: Ten

Q.16: Is -5 an integer? Yes or No.

Answer: Yes

Q.17: The value of pi is equal to:

Answer: 22/7 or 3.14

Q.18: 9 x 7 is equal to:

Q.19: Is triangle a two-dimensional or three-dimensional shape?

Answer: A two-dimensional shape

Q.20: An equilateral triangle has two of its sides equal. True or false?

Answer: False

All the sides of the equilateral triangle are equal.

Q.21: 10 is a natural number. True or false?

Answer: True

Q.22: -10 is a whole number. True or false?

Q.23: 8 raised to the power 0 is equal to:

Q.24: The largest 4 digit number is:

Answer: 9999

Q.25: The smallest 4-digit number is:

Answer: 1000

Q.26: The square of 8 is equal to:

8 2 = 8 x 8 = 64

Q.27: The square root of 5 is:

Answer: 2.23

Q.28: 3 is a perfect square. True or False?

Answer: False.

Q.29: Cube of 5 is equal to:

Answer: 125

5 3 = 5 x 5 x 5 = 125

Q.30: Cube root of 1331 is:

1331 = 11 x 11 x 11 = 11 3

Q.31: 27 is a perfect cube. True or False?

27 = 3 x 3 x 3= 3 3

Q.32: A square has all its angles equal to:

Answer: 90 degrees

Q.33: The area of rectangle is equal to:

Answer: Length x Breadth

Q.34: If a is the side of cube, then the volume of the cube is:

Answer: a 3

Q.35: A regular polygon has all its sides:

Answer: Equal

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20 Grade-School Math Questions So Hard You'll Wonder How You Graduated

Seriously, who can do these?!

Unless you grew up to be an engineer, a banker, or an accountant, odds are that elementary and middle school math were the bane of your existence. You would study relentlessly for weeks for those silly standardized tests—and yet, come exam day, you'd still somehow have no idea what any of the equations or hard math problems were asking for. Trust us, we get it.

While logic might lead you to believe that your math skills have naturally gotten better as you've aged, the unfortunate reality is that, unless you've been solving algebra and geometry problems on a daily basis, the opposite is more likely the case.

Don't believe us? Then put your number crunching wisdom to the test with these tricky math questions taken straight from grade school tests and homework assignments and see for yourself.

1. Question: What is the number of the parking space covered by the car?

This tricky math problem went viral a few years back after it appeared on an entrance exam in Hong Kong… for six-year-olds. Supposedly the students had just 20 seconds to solve the problem!

Answer: 87.

Believe it or not, this "math" question actually requires no math whatsoever. If you flip the image upside down, you'll see that what you're dealing with is a simple number sequence.

2. Question: Replace the question mark in the above problem with the appropriate number.

This problem shouldn't be  too difficult to solve if you play a lot of sudoku.

All of the numbers in every row and column add up to 15! (Also, 6 is the only number not represented out of numbers 1 through 9.)

3. Question: Find the equivalent number.

This problem comes straight from a standardized test given in New York in 2014.

You're forgiven if you don't remember exactly how exponents work. In order to solve this problem, you simply need to subtract the exponents (4-2) and solve for 3 2 , which expands into 3 x 3 and equals 9.

4. Question: How many small dogs are signed up to compete in the dog show?

This question comes directly from a second grader's math homework. Yikes.

Answer: 42.5 dogs.

In order to figure out how many small dogs are competing, you have to subtract 36 from 49 and then divide that answer, 13, by 2, to get 6.5 dogs, or the number of big dogs competing. But you're not done yet! You then have to add 6.5 to 36 to get the number of small dogs competing, which is 42.5. Of course, it's not actually possible for half a dog to compete in a dog show, but for the sake of this math problem let's assume that it is.

5. Question: Find the area of the red triangle.

This question was used in China to identify gifted 5th graders. Supposedly, some of the smart students were able to solve this in less than one minute.

In order to solve this problem, you need to understand how the area of a parallelogram works. If you already know how the area of a parallelogram and the area of a triangle are related, then adding 79 and 10 and subsequently subtracting 72 and 8 to get 9 should make sense—but if you're still confused, then check out this YouTube video for a more in-depth explanation.

6. Question: How tall is the table?

YouTuber MindYourDecisions adapted this mind-boggling math question from a similar one found on an elementary school student's homework in China.

Answer: 150 cm.

Since one measurement includes the cat's height and subtracts the turtle's and the other does the opposite, you can essentially just act like the two animals aren't there. Therefore, all you have to do is add the two measurements—170 cm and 130 cm—together and divided them by 2 to get the table's height, 150 cm.

7. Question: If the cost of a bat and a baseball combined is $1.10 and the bat costs $1.00 more than the ball, how much is the ball?

Answer: $0.05.

Think back to that problem about the dogs at the dog show and use the same logic to solve this problem. All you have to do is subtract $1.00 from $1.10 and then divide that answer, $0.10 by 2, to get your final answer, $0.05.

8. Question: When is Cheryl's birthday?

If you're having trouble reading that, see here:

"Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15           May 16           May 19

June 17           June 18

July 14            July 16

August 14       August 15       August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don't know when Cheryl's birthday is, but I know that Bernard doesn't not know too.

Bernard: At first I don't know when Cheryl's birthday is, but I know now.

Albert: Then I also know when Cheryl's birthday is.

So when is Cheryl's birthday?"

It's unclear why Cheryl couldn't just tell both Albert and Bernard the month and day she was born, but that's irrelevant to solving this problem.

Answer: July 16.

Confused about how one could possibly find any answer to this question? Don't worry, so was most of the world when this question, taken from a Singapore and Asian Schools Math Olympiad competition, went viral a few years ago. Thankfully, though, the  New York Times  explains step-by-step how to get to July 16, and you can read their detailed deduction here.

9. Question: Find the missing letter.

This one comes from a  first grader's  homework.

Answer: The missing letter is J.

When you add together the values given for S, B, and G, the sum comes out to 40, and making the missing letter J (which has a value of 14) makes the other diagonal's sum the same.

10. Question: Solve the equation.

This problem might look easy, but a surprising number of adults are unable to solve it correctly.

Start by solving the division part of the equation. In order to do that, in case you forgot, you have to flip the fraction and switch from division to multiplication, thus getting 3 x 3 = 9. Now you have 9 – 9 + 1, and from there you can simply work from left to right and get your final answer: 1.

11. Question: Where should a line be drawn to make the below equation accurate?

5 + 5 + 5 + 5 = 555.

Answer: A line should be drawn on a "+" sign.

When you draw a slanted line in the upper left quadrant of a "+," it becomes the number 4 and the equation thusly becomes 5 + 545 + 5 = 555.

12. Question: Solve the unfinished equation.

Try to figure out what all of the equations have in common.

Answer: 4 = 256.

The formula used in each equation is 4 x  = Y. So, 4 1  = 4, 4 2  = 16, 4 3  = 64, and 4 4  = 256.

13. Question: How many triangles are in the image above?

When  Best Life  first wrote about this deceiving question, we had to ask a mathematician to explain the answer!

Answer: 18.

Some people get stumped by the triangles hiding inside of the triangles and others forget to include the giant triangle housing all of the others. Either way, very few individuals—even math teachers—have been able to find the correct answer to this problem. And for more questions that will put your former education to the test, check out these  30 Questions You'd Need to Ace to Pass 6th Grade Geography.

14. Question: Add 8.563 and 4.8292.

Adding two decimals together is easier than it looks.

Answer: 13.3922.

Don't let the fact that 8.563 has fewer numberrs than 4.8292 trip you up. All you have to do is add a 0 to the end of 8.563 and then add like you normally would.

15. Question: There is a patch of lily pads on a lake. Every day, the patch doubles in size…

… If it takes 48 days for the patch to cover the entire lake, how long would it take for the patch to cover half of the lake?

Answer: 47 days.

Most people automatically assume that half of the lake would be covered in half the time, but this assumption is wrong. Since the patch of pads  doubles in size every day, the lake would be half covered just one day before it was covered entirely.

16. Question: How many feet are in a mile?

This elementary school-level problem is a little less problem solving and a little more memorization.

Answer: 5,280.

This was one of the questions featured on the popular show  Are You Smarter Than a 5th Grader?

17. Question: What value of "x" makes the equation below true?

-15 + (-5x) = 0

Answer: -3.

You'd be forgiven for thinking that the answer was 3. However, since the number alongside x is negative, we need x to be negative as well in order to get to 0. Therefore, x has to be -3.

18. Question: What is 1.92 divided by 3?

You might need to ask your kids for help on this one.

Answer: 0.64.

In order to solve this seemingly simple problem, you need to remove the decimal from 1.92 and act like it isn't there. Once you've divided 192 by 3 to get 64, you can put the decimal place back where it belongs and get your final answer of 0.64.

19. Question: Solve the math equation above.

Don't forget about PEMDAS!

Using PEMDAS (an acronym laying out the order in which you solve it: "parenthesis, exponents, multiplication, division, addition, subtraction"), you would first solve the addition inside of the parentheses (1 + 2 = 3), and from there finish the equation as it's written from left to right.

20. Question: How many zombies are there?

Finding the answer to this final question will require using fractions.

Answer: 34.

Since we know that there are two zombies for every three humans and that 2 + 3 = 5, we can divide 85 by 5 to figure out that in total, there are 17 groups of humans and zombies. From there, we can then multiply 17 by 2 and 3 and learn that there are 34 zombies and 51 humans respectively. Not too bad, right?

To discover more amazing secrets about living your best life,  click here  to follow us on Instagram!

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Pythagoras Theorem Questions

Welcome to our Pythagoras' Theorem Questions area. Here you will find help, support and questions to help you master Pythagoras' Theorem and apply it.

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Pythagoras' Theorem Questions

Here you will find our support page to help you learn to use and apply Pythagoras' theorem.

Please note: Pythagoras' Theorem is also called the Pythagorean Theorem

There are a range of sheets involving finding missing sides of right triangles, testing right triangles and solving word problems using Pythagoras' theorem.

Using these sheets will help your child to:

• learn Pythagoras' right triangle theorem;
• use and apply the theorem in a range of contexts to solve problems.

Pythagoras' Theorem

Pythagoras' Theorem - in more detail

Pythagoras' theorem states that in a right triangle (or right-angled triangle) the sum of the squares of the two smaller sides of the triangle is equal to the square of the hypotenuse.

In other words, \[ a^2 + b^2 = c^2 \]

where c is the hypotenuse (the longest side) and a and b are the other sides of the right triangle.

What does this mean?

This means that for any right triangle, the orange square (which is the square made using the longest side) has the same area as the other two blue squares added together.

Other formulas that can be deduced from the Pythagorean theorem

As a result of the formula \[ a^2 + b^2 = c^2 \] we can also deduce that:

• \[ b^2 = c^2 - a^2 \]
• \[ a^2 = c^2 - b^2 \]
• \[ c = \sqrt{a^2 + b^2} \]
• \[ b = \sqrt {c^2 - a^2} \]
• \[ a = \sqrt {c^2 - b^2} \]

Pythagarean Theorem Examples

Example 1) find the length of the missing side..

In this example, we need to find the hypotenuse (longest side of a right triangle).

So using pythagoras, the sum of the two smaller squares is equal to the square of the hypotenuse.

This gives us \[ 4^2 + 6^2 = ?^2 \]

So \[ ?^2 = 16 + 36 = 52 \]

This gives us \[ ? = \sqrt {52} = 7.21 \; cm \; to \; 2 \; decimal \; places \]

Example 2) Find the length of the missing side.

In this example, we need to find the length of the base of the triangle, given the other two sides.

This gives us \[ ?^2 + 5^2 = 8^2 \]

So \[ ?^2 = 8^2 - 5^2 = 64 - 25 = 39 \]

This gives us \[ ? = \sqrt {39} = 6.25 \; cm \; to \; 2 \; decimal \; places \]

Pythagoras' Theorem Question Worksheets

The following questions involve using Pythagoras' theorem to find the missing side of a right triangle.

The first sheet involves finding the hypotenuse only.

A range of different measurement units have been used in the triangles, which are not drawn to scale.

• Pythagoras Questions Sheet 1
• PDF version
• Pythagoras Questions Sheet 2
• Pythagoras Questions Sheet 3
• Pythagoras Questions Sheet 4

Pythagoras' Theorem Questions - Testing Right Triangles

The following questions involve using Pythagoras' theorem to find out whether or not a triangle is a right triangle, (whether the triangle has a right angle).

If Pythagoras' theorem is true for the triangle, and c 2 = a 2 + b 2 then the triangle is a right triangle.

If Pythagoras' theorem is false for the triangle, and c 2 = a 2 + b 2 then the triangle is not a right triangle.

• Pythagoras Triangle Test Sheet 1
• Pythagoras Triangle Test Sheet 2

Pythagoras' Theorem Questions - Word Problems

The following questions involve using Pythagoras' theorem to solve a range of word problems involving 'real-life' type questions.

On the first sheet, only the hypotenuse needs to be found, given the measurements of the other sides.

Illustrations have been provided to support students solving these word problems.

• Pythagoras Theorem Word Problems 1
• Pythagoras Theorem Word Problems 2

Geometry Formulas

• Geometry Formula Sheet

Here you will find a support page packed with a range of geometric formula.

Included in this page are formula for:

• areas and volumes of 2d and 3d shapes
• interior angles of polygons
• angles of 2d shapes
• triangle formulas and theorems

This page will provide a useful reference for anyone needing a geometric formula.

Triangle Formulas

Here you will find a support page to help you understand some of the special features that triangles have, particularly right triangles.

Using this support page will help you to:

• understand the different types and properties of triangles;
• understand how to find the area of a triangle;
• know and use Pythagoras' Theorem.

All the free printable geometry worksheets in this section support the Elementary Math Benchmarks.

• Geometry Formulas Triangles

Here you will find a range of geometry cheat sheets to help you answer a range of geometry questions.

The sheets contain information about angles, types and properties of 2d and 3d shapes, and also common formulas associated with 2d and 3d shapes.

Included in this page are:

• images of common 2d and 3d shapes;
• properties of 2d and 3d shapes;
• formulas involving 2d shapes, such as area and perimeter, pythagoras' theorem, trigonometry laws, etc;
• formulas involving 3d shapes about volume and surface area.

Using the sheets in this section will help you understand and answer a range of geometry questions.

How to Print or Save these sheets 🖶

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Top 5 Trickiest Mathematics Questions From Around the World

Math(s) can be a tricky subject for many students. But some questions are trickier than others.

Put on your thinking caps because we searched the internet for the top 5 trickiest mathematics questions from all around the world.

Solutions are provided at the end of all the questions (but no peeking).

If you’re up for an extra challenge, we’ve even got a bonus question at the end.

But before that… a quick announcement. World Maths Day – the world’s largest mathematics competition is back!

World Maths Day, happening on 8 March 2023, is a global celebration of mathematics where millions of students aged 5 to 18 across the world compete in Live Mathletics challenges. It’s all-inclusive, free, and open to schools as well as students learning from home. Learn more about it here .

Now, let’s jump in!

1. People on a Train 🚂

Country of origin: England

In a since-deleted tweet, a mum from England tweeted this word problem in a test meant for kids aged 6 to 7 in 2016. It went viral and even some adults were having trouble figuring out the answer.

The Question:

There were some people on a train.

19 people get off the train at the first stop.

17 people get on the train.

Now there are 63 people on the train. How many people were on the train to begin with?

2. You’ll Never Forget Cheryl’s Birthday 📅

Country of origin: Singapore

Problems that test logical reasoning are common in Math(s) Olympiads. But this question from the 2015 Singapore and Asian Schools Math Olympiad contest for students 14 to 15 years old got the whole world stumped.

Albert and Bernard just became friends with Cheryl, and they want to know when her birthday is.

Cheryl gives them a list of 10 possible dates:

• May 15, May 16, May 19
• June 17, June 18
• July 14, July 16
• August 14, August 15, August 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too.

Bernard: At first I don’t know when Cheryl’s birthday is, but I know now.

Albert: Then I also know when Cheryl’s birthday is.

So when is Cheryl’s birthday?

3. Taming the Snake 🐍

Country of origin: Vietnam 

This question is not only tricky but might also take a while. According to VNEXPRESS, this puzzle is meant for third graders/year 3 students (8 year olds) in Vietnam!

The Puzzle:

Image source: VN Express

All you have to do is use the digit 1 to 9 once to fill in the boxes to make the entire equation equal to 66. The expression should be read from left to right.

Sounds easy? Not quite.

In case you’re wondering, the boxes containing colon represents division.

4. Remember Where You Parked Your Car 🚗

Country of origin: Hong Kong

This problem has been around for a while but resurfaced on an elementary/primary school entrance exam in Hong Kong.

Apparently, six-year-olds were expected to know the answer in 20 seconds or less.

What is the car’s parking spot number?

5. The Red Triangle 🔺

Country of origin: China

This question came from China and was used to identify gifted fifth grade/year 5 students (10 to 11 years old). It’s said that some of them were able to solve this question in less than one minute!

ABCD is a parallelogram. In the diagram, the areas of yellow regions are 8, 10, 72 and 79.

Find the area of the red triangle. The diagram is not to scale.

Image source: Mind Your Decisions

BONUS Tricky Math(s) Question

If you still have head space for one more, try this.

6. A Mass of Money: Helen and Ivan’s coins 💰

In 2021, a Primary School Leaving Exam mathematics question left some 12-year-old students in tears. Supposedly, this question was meant to be solved in a matter of minutes, as it is only allocated 4 marks in total.

Note: This two-part question could have been recalled from memory and rewritten by an adult, which could explain the grammatical errors.

Helen and Ivan had the same number of coins.

Helen had a number of 50-cent coins, and 64 20-cent coins. These coins had a mass of 1.134kg.

Ivan had a number of 50-cent coins and 104 20-cent coins.

(a) Who has more money in coins and by how much?

(b) given that each 50-cent coin is 2.7g heavier than a 20-cent coin, what is the mass of Ivan’s coins in kilograms?

Could You Solve These Tricky Mathematics Questions?

Or were you confused and stumped? Well, you’re not alone.

We had a really tough time understanding and solving them too.

If you’re a teacher and looking for problem and reasoning questions , consider a mathematics resource to sharpen your student’s logical thinking skills.

Now let’s get to the answers…

Question 1 answer.

19 people getting off the train can be represented by -19, and 17 people getting on the train as +17.

-19 + 17 = 2, meaning that there was a net loss of two people.

Originally, the train had 2 more people.

So if there are 63 people on the train now, that means there were 65 people to begin with.

Question 2 Answer

You can solve this by the process of elimination, based on what each person says.

Let’s go through the information line by line.

[Line 7] Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.

This is an important piece of information because it tells us that Albert knows the month , and Bernard knows the day .

So Albert knows it’s either May, June, July or August, and Bernard knows that it’s either 14, 15, 16, 17, 18 or 19.

[Line 8] Albert: I don’t know when Cheryl’s birthday is, but I know that Bernard doesn’t know too .

The second part is the clue. The fact that Albert claims that Bernard doesn’t know means it can’t be 18 or 19. Why?

If it were 19, then Bernard would know the exact birthday, as May is the only date with 19.

If Bernard was told the date was 18, he would also know that the birthday must be June 18, as that’s the only date with 18.

So you can rule out May 19 and June 18.

But how is Albert sure that Bernard didn’t hear 18 or 19?

It must be because Albert knows the birthday is not in May or June.

If Albert was told the month was May, he couldn’t be sure that Bernard wasn’t thinking of the number 19. Therefore, you can cross out May.

And if Albert was told the month of June, he couldn’t’ be sure if Bernard wasn’t thinking of the number 17. So June is also out.

In other words, Albert was told either July or August .

Based on the above information, you can eliminate these five dates – May 15, May 16, May 19, June 17 and June 18.

Dates left: July 14, July 16, August 14, August 15 and August 17.

[Line 9] Bernard: At first I don’t know when Cheryl’s birthday is, but now I know.

Upon hearing Albert’s statement, Bernard now figures this out.

If Bernard was told the date was 14, it would still be ambiguous whether the month was July or August. So you can rule out he was not told 14.

You are now left with three dates – July 16, August 15 and August 17.

[Line 10] Albert: Then I also know when Cheryl’s birthday is.

Albert couldn’t have been told it was August, as there are two dates in August. So you can deduce that he must have been told it’s July.

Therefore, the answer is July 16 .

Question 3 Answer

Let’s start by breaking the puzzle into bite-size pieces, one step at a time.

First, write the expression in the normal way you usually write mathematical expressions. This makes it easier to put in the numbers.

__ + 13 × __ ÷ __ + __ + 12 × __ – __ – 11 + __ × __ ÷ __ – 10 = 66

Next, let’s look at how many ways are there to put the numbers 1 to 9 in these 9 different boxes.

You can put 9 different numbers in the first box.

So that’s 9 possibilities in the first box, 8 possibilities in the second box, followed by 7 boxes in the third box and so forth.

Applying this logic, you will have one less possibility for each box, until we get to the last box.

In total, there are 9 factorial (9 × 8 × 7 × 6 × 5 × 4 × 3 × 2 × 1 = 9!) or 362,880 possibilities .

Now that’s a lot of possibilities to try and work by purely guessing and checking.

So let’s try working out the solution logically.

Remember the BEDMAS/BIDMAS/PEDMAS/PEMDAS rule you learnt in school?

To respect the order of operations, add parentheses or brackets to the equation. This means that multiplication or division comes before addition or subtraction.

__ + ( 13 × __ ÷ __ ) + __ + ( 12 × __ ) – __ – 11 + ( __ × __ ÷ __ ) – 10 = 66

Now it’s time to fill in some numbers to guess and check our assumptions.

What if you first used the numbers 1 to 9, from left to right ?

1 + (13 × 2 ÷ 3 ) + 4 + (12 × 5 ) – 6 – 11 + ( 7 × 8 ÷ 9 ) – 10 = 52.88…

Hey, that’s pretty close to 66!

What if you wrote the numbers in descending order , from 9 to 1?

9 + (13 × 8 ÷ 7 ) + 6 + (12 × 5 ) – 4 – 11 + ( 3 × 2 ÷ 1 ) – 10 = 70.85…

That also gets you pretty close to the answer.

So how can you modify this expression to get to 66? The key is to look at the numbers and their positions.

In the next few steps, we used trial and error – testing and moving the numbers around until we got to 66.

Here’s one solution we got:

9 + (13 × 4 ÷ 8 ) + 5 + (12 × 6 ) – 7 – 11 + ( 1 × 3 ÷ 2 ) – 10 = 66

Now for the keen observers out there, you’d notice that you can switch the numbers that are being added, to generate another solution.

For example:

9 + (13 × 4 ÷ 8) + 5 + (12 × 6) – 7 – 11 + (1 × 3 ÷ 2) – 10 = 66 OR (switch 5 and 9) 5 + (13 × 4 ÷ 8) + 9 + (12 × 6) – 7 – 11 + (1 × 3 ÷ 2) – 10 = 66

Similarly, you can switch the numbers that are multiplied, and it won’t affect the final answer.

9 + (13 × 4 ÷ 8) + 5 + (12 × 6) – 7 – 11 + ( 1 × 3 ÷ 2) – 10 = 66 OR (switch 1 and 3) 9 + (13 × 4 ÷ 8) + 5 + (12 × 6) – 7 – 11 + ( 3 × 1 ÷ 2) – 10 = 66

This means anytime you come up with one way to solve it, you can generate a total of four ways – because multipclation and addition are commutative (it doesn’t what the order of the numbers are, the answer is the same).

In fact, there are multiple answers to this puzzle. 136 to be exact. How do we know?

Now, that’s a problem to solve for another time. 😉

Question 4 Answer

The ‘trick’ to this question is that it requires no math(s) at all!

All you have to do is to look at it from a different perspective – literally.

Turn the question upside down, and you’ll see that it’s a simple number sequence, with the answer being 87.

Question 5 Answer

Even though it looks complicated, this question can actually be solved with a simple calculation: 79 + 10 – 72 – 8 = 9

Wait, what? But how?

To get there, you need to understand basic arithmetic and know that the area of a parallelogram and the area of a triangle are related.

The ‘secret’ is to identify triangles with areas that are half of the parallelogram.

The area of a triangle is (base × height) ÷ 2, and the area of a parallelogram is base × height.

A triangle whose base equals one side of the parallelogram, and whose height reaches the opposite side of the parallelogram, has exactly half the area of a parallelogram.

This is true for a pair of triangles as well – if the pair of triangles span one side and if their heights reach the opposite side.

To make solving this easier, you can start by labelling the unknown areas with letters a to f . And let the area of the red triangle be x .

Presh Talwalkar from Mind You Decisions, breaks down the solution in his video here .

Question 6 Answer (Part a)

The key is to remember that Helen and Ivan have the same number of coins.

Let’s look and compare the total number of coins for each type.

Ivan has 40 more 20-cent coins than Helen. For them to have the same number of coins, you have to ‘balance’ this out in terms of the 50-cent coins.

This means Helen must have 40 more of the 50-cent coins than Ivan.

Let’s now compare the amount of money of each coin type that Helen has, minus that of Ivan.

Since Helen has 40 fewer (104 – 64) of the 20-cent coins, so Helen will have:

– 40 × 0.2 = – 8

This means she has $8 less than Ivan (in 20-cent coins).

On the other hand, Helen has 40 more of the 50-cent coins than Ivan. So she will have:

+ 40 × 0.5 = 20

This means she has $20 more than Ivan (in 50-cent coins).

Now, you can add this together to find out how much more or less money Helen has.

– 8 + 20 = 12

Therefore, Helen has $12 more than Ivan.

Question 6 Answer (Part b):

The total mass of Helen’s coin is 1.134kg. And you know that a 50-cent coin is 2.7g heavier than a 20-cent coin.

From the first part of the question, you can see that if you had Helen’s coins, you can ‘exchange’ 40 of the 50-cent coins for 40 of the 20-cent coins, that will be the total coins Ivan has. And you can get the weight difference from that.

Let’s compare the weight of Helen’s coins to Ivan’s coins.

In terms of the 20-cent coins, subtract 40 of the 20-cent coins, multiplied by the weight of the coins.

– 40 × 0.2 weight

In terms of the 50-cent coins, add 40 of the 50-cent coins, multiplied by the weight.

+40 × 0.5 weight

So the net impact of this, Helen compared to Ivan, has 40 more of the heavier coins – 40 more of the 50-cent coins, compared to the 20-cent coins than Ivan.

+ 40 × 0.5 weight / 40 × (0.5 – 0.2 weight)

You know the difference in weight between 50-cent and 20-cent coins is 2.7 grams. Therefore, you can substitute that in the equation.

+ 40 × 0.5 weight / 40 × (2.7 g) –> 40 × (2.7 g) = 108g

So Helen’s weight of coins is 108 g more than Ivan.

To get Ivan’s weight, we take Helen’s coins and subtract by 108g.

1134g – 108g = 1026g

Convert that to kilograms to get the answer, 1.026 kg .

How did you fare? Share this with your students or friends who love a great math(s) challenge!

If you’re looking to challenge your students’ mathematical fluency , why not take part if World Maths Day – the world’s largest online competition ?

What is World Maths Day?

World Maths Day is a global celebration of mathematics where millions of students aged 5 to 18 across the world compete in Live Mathletics challenges. It’s all-inclusive, free, and open to schools as well as students learning from home.

If you don’t have a Mathletics account, you can sign up for a free World Maths Day account here.

Have any questions? Check out the World Maths Day FAQ page for more information or contact us here .

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94 Clever Riddles for Kids, From the Easy to the Seriously Tricky

We bet some adults will even be stumped by these brainteasers.

Animal Riddles for Kids

Funny riddles for little kids, food riddles for kids, math riddles for kids.

And getting loads of laughs isn't just one benefit of solving riddles with your kids. Riddles, known as a statement or question that has multiple meanings and needs to be solved, have been credited with helping kids work on their logic and critical thinking skills , practice their vocabulary, stretch their problem-solving muscles and sometimes even give them a good laugh or an a-ha moment when they've reached the solution.

Our list, which has a good mix of easy-to-answer options as well as head-scratchers that even adults might struggle to figure out, not only can keep the young ones occupied on their own when you're stuck in line somewhere or need a quick fix to keep the kid's busy, but they also provide the opportunity for collaboration and quality time if you decide to take the list together.

Tricky Riddles for Kids

Q: Grandpa went for a walk, and it started raining. He forgot to bring an umbrella and didn’t have a hat. When he got home, his clothes were soaking wet, but not a hair on his head was wet. How was this possible? A: Grandpa is bald.

Q: I speak without a mouth and hear without ears. I have nobody, but I come alive with the wind. What am I? A: An echo.

Q: What is full of holes but still holds water? A: A sponge.

Q: What can you catch but not throw? A: A cold.

Q: What can run but never walks, has a mouth but never talks, has a head but never weeps, and has a bed but never sleeps? A: A river.

Q: In a one-story house at the corner of the road, the bedrooms were yellow, the kitchen was orange, the living room was red, the garage was blue, the entry hall was green, and the sitting room was purple. What color were the stairs? A: There’s no color because there are no stairs — it’s a one-story house.

Q: What starts with a ‘P’, ends with an ‘E’, and has thousands of letters? A: A post office

Q: Give me a drink, and I will die. Feed me, and I'll get bigger. What am I? A: A fire.

Q: What word begins with E and ends with E, but only has one letter? A: Envelope.

Q: What appears once in a minute, twice in a moment, but not once in a thousand years? A: The letter "M."

Q: What has many rings but no fingers? A: A telephone.

Q: What goes up but never comes back down? A: Your age.

Q: I go all around the world, but never leave the corner. What am I? A: A stamp.

Q: If you drop a yellow hat in the Red Sea, what does it become? A: Wet.

Q: I’m always on the dinner table, but you don’t get to eat me. What am I? A: Plates and silverware.

Q: What goes in a birdbath but never gets wet? A: The bird's shadow.

Q: What two things can you never eat for breakfast? A: Lunch and dinner.

Q: If you drop me, I’m sure to crack, but smile at me and I’ll smile back. What am I? A: A mirror.

Q: What has hands and a face, but no arms or legs? A: A clock.

Q: You’ll find me in Mercury, Earth, Mars and Jupiter, but not in Venus or Neptune. What am I? A: The letter “R.”

Q: I’m light as a feather, yet the strongest person can’t hold me for five minutes. What am I? A: Your breath.

Q: I have cities, but no houses. I have forests, but no trees. I have water, but no fish. What am I? A: A map.

Q: What can you break, even if you never pick it up or touch it? A: A promise.

Q: What is yours but mostly used by others? A: Your name.

Q: Which question can you never answer "yes" to? A: "Are you asleep?"

Q: What's something that, the more you take, the more you leave behind? A: Footsteps.

Q: I have no sword, I have no spear, yet rule a horde which many fear, my soldiers fight with a wicked sting, I rule with might, yet am no king. What am I? A: A queen bee.

Q: I have arms that are longer than my legs. I have been taught sign language to communicate. Who am I? A: A gorilla.

Q: I like to stay awake at night and sleep during the day. What am I? A: An owl.

Q: My skin is green and slipper, I have four legs and webbed feet, I hop on land and swim underwater, I love bugs and little fish to eat. What am I? A: A frog.

Q: The alphabet goes from A to Z, but I go Z to A. What am I? A: A zebra.

Q: A rooster is sitting on the roof of a barn facing west. If it laid an egg, would the egg roll to the north or to the south? A: It's impossible — roosters don't lay eggs.

Q: A cowgirl road into town on Friday. Three days later, she left on Friday. How is that possible? A: Friday is the name of her horse.

Q: What kind of lion never roars? A: A dandelion.

Q: What has a thousand needles but cannot sew? A: A porcupine.

Q: Without me Thanksgiving and Christmas are incomplete, when I’m on the table everyone tends to overeat. What am I? A: Turkey.

Q: What’s bright orange with green on top and sounds like a parrot? A: A carrot.

Q: Why do bees have sticky hair? A: Because they use their honeycombs.

Q: What do you call a bear with no teeth? A: A gummy bear.

Q: What’s black, white and blue? A: A sad zebra.

Q: I jump when I walk and sit when I stand. What am I? A: Kangaroo.

Q: I grow down as I grow up. What am I? A: A goose. Goose feathers are called down.

Q: I’m the father of fruits. What am I? A: A papa-ya.

Q: Why are teddy bears never hungry? A: Because they are always stuffed.

Q: Cats have four, bugs have four, but school has six. What are they? A: Letters.

Q: Sam's parents have three kids. Their names are Huey, Dewey, and _____? A: Sam!

Q: Nobody empties me, but I never stay full for long. What am I? A: The moon.

Q: What do you get when you cross a snowman and a vampire? A: Frostbite.

Q: What’s really easy to get into, and hard to get out of? A: Trouble.

Q: What animal can jump higher than a building? A: Any animal that can jump — buildings don’t jump, silly!

Q: Where would you take a sick boat? A: To the dock.

Q: What did the zero say to the eight? A: “Nice belt!”

Q: What gets wet while drying? A: A towel.

Q: I’m tall when I’m young, and I’m short when I’m old. What am I? A: A candle.

Q: What room do ghosts avoid? A: The living room.

Q: I can be cracked or played; told or made. What am I? A: A joke!

Q: What has a head and a tail but no body? A: A coin.

Q: I sometimes run, but I cannot walk. What am I? A: Your nose.

Q: What has four fingers and a thumb but isn’t alive? A: A glove

Q: What has no beginning, end or middle? A: A doughnut.

Q: Although I may have eyes, I cannot see. I have a round brown face with lots of acne. What am I? A: A potato.

Q: What kind of dog has no tail? A: A hot dog.

Q: I am a bird, I am a fruit and I am a person. What am I? A: Kiwi.

Q: What fruit never ever wants to be alone? A: A pear.

Q: I can be bitter or sweet, but I'm always a treat; in a bar or a cake, I'm something to eat. What am I? A: Chocolate.

Q: I can be yellow or blue, soft or hard; on a burger or mac, I’m often starred. What am I? A: Cheese.

Q: First, you throw away my outside and cook the inside. Then you eat my outside and throw away the inside. What am I? A: Corn.

Q: What kind of cheese is made backwards? A: Edam. Made is M-A-D-E, Edam is E-D-A-M, or "made" backwards.

Q: What has a head but no eyes, nose or mouth? A: Lettuce.

Q: I'm red and small, and I have a heart of stone. What am I? A: A cherry.

Q: When I’m ripe, I’m green, when you eat me, I’m red, and when you spit me out, I’m black. What am I? A: A watermelon.

Q: What fruit can you never cheer up? A: A blueberry.

Q: What has to be broken before you can use it? A: An egg

Q: What kind of foods are the most fun at parties? A: Fungi.

Q: What is the richest nut? A: A cash-ew.

Q: Why did the citrus tree go to the hospital? A: Lemon-aid.

Q: You cut me, slice me, dice me, and all the while, you cry. What am I? A: An onion.

Q: What kind of room has no doors or windows? A: A mushroom.

Q: What kind of apples do computers prefer? A: Macintosh.

Q: What kind of cup doesn’t hold water? A: A cupcake.

Q: If there are seven oranges and you take three away, how many oranges do you have? A: Three, since that's how many you took.

Q: How many seconds are in a year? A: Twelve — January 2nd, February 2nd, March 2nd...

Q: How many letters are there in the alphabet? A: There are 11: three in "the" and eight in "alphabet."

Q: Ms. Smith has four daughters. Each daughter has a brother. How many kids are there in total? A: Five, there are four daughters and one son. Each daughter has the same brother.

Q: When things go wrong, what can you always count on? A: Your fingers.

Q: What did the triangle say to the circle? A: You are pointless.

Q: You have a basket that's one foot in diameter and one foot deep. How many apples can you fit in the empty basket? A: Only one, because then it's not empty anymore.

Q: If two’s a company, and three’s a crowd, what are four and five? A: Nine!

Q: Why was 6 afraid of 7? A: Because 7, 8 (ate), 9!

Q: Four legs up, four legs down, soft in the middle, hard all around. What am I? A: A bed.

Q: A word I know, six letters it contains, remove one letter and 12 remains, what is it? A: Dozens.

Q: What month of the year has 28 days? A: All of them!

Q: The more you take, the more you leave behind. What am I? A: Footsteps.

@media(max-width: 64rem){.css-o9j0dn:before{margin-bottom:0.5rem;margin-right:0.625rem;color:#ffffff;width:1.25rem;bottom:-0.2rem;height:1.25rem;content:'_';display:inline-block;position:relative;line-height:1;background-repeat:no-repeat;}.loaded .css-o9j0dn:before{background-image:url(/_assets/design-tokens/goodhousekeeping/static/images/Clover.5c7a1a0.svg);}}@media(min-width: 48rem){.loaded .css-o9j0dn:before{background-image:url(/_assets/design-tokens/goodhousekeeping/static/images/Clover.5c7a1a0.svg);}} Parenting Tips & Advice

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Welcome to the daily solving of our PROBLEM OF THE DAY with Ayush Tripathi. We will discuss the entire problem step-by-step and work towards developing an optimized solution. This will not only help you brush up on your concepts of Matrix but also build up problem-solving skills. A matrix is constructed of size n*n and given an integer ‘ q’. The value at every cell of the matrix is given as, M(i,j) = i+j, where ‘ M(i,j) ' is the value of a cell, ‘ i ’ is the row number, and ‘ j’ is the column number. Return the number of cells having value ‘ q ’.

Note: Assume, the array is in 1-based indexing.

Input: n = 4, q = 7 Output: 2 Explanation: Matrix becomes 2 3 4 5 3 4 5 6 4 5 6 7 5 6 7 8 The count of 7 is 2.

Give the problem a try before going through the video. All the best!!! Problem Link: https://practice.geeksforgeeks.org/problems/summed-matrix5834/1