Maths Puzzles

The following puzzles are from the Transum monthly newsletters and podcasts.

Maths Equipment

What percentage of the class brought all the required maths equipment to the lesson?

What is the letter D worth?

From the clues about A, B and C can you work out the value of D?

Easter Egg Evaluation

What is the largest number of eggs that cannot be purchased using a combination of the given basket sizes?

Leap Year February

What birthday did Attika celebrate in the last leap year of the last century?

Justin's New Year's Resolution

How many days in January will Justin be able to go for a jog?

Mean Spending On Christmas Presents

Work out the cost of the most expensive gift given the mean cost and other clues.

End of Squares and Cubes

How many positive two-digit numbers are there whose square and cube both end in the same digit?

Whopping Million

Find two whole numbers, not containing zeros, that when multiplied, give a million.

Divided Dartboard

A dartboard splits in two. One piece's numbers sum to twice the other's. Where's the break?

Calamity Cousins

Work out the range of the ages of the cousins given the average clues.


If x and y are positive integers and x + xy + y = 90, what is the sum of x and y?

Indices are powerful exponents!

If x squared equals sixteen to the power of x. Find the value of x.

Letters in a Sentence

Write a number in words in the gap in the sentence that will make the statement true.

Cupcakes and Easter Eggs

Work out how many children there were eating cupcakes from the given clues.

One Hundred Puzzle

Can you make 100 from four sevens and a zero?

Palindromic Numbers

Work out Mr Wheeler's average speed given the palindromic numbers seen on his odometer.

Six Three-Letter Words

Work out the teacher's favourite word from the statements made by the clever students.

Coloured Ornaments

How many ornaments are on the tree and how many of each colour are there?

Same Probability

Why are the probabilities the same of picking two balls with an odd sum from two different pots?

Settle Debts

What is the best way to settle the debts of the four friends?

Viral Maths

What is the correct result of the calculation that has become a viral talking point on the internet?

Holiday Island Weather

Work out the length of my holiday from the clues about the weather.

Weighted Puzzle

What four weights would enable me to use the balance scales to weigh any object from 1 to 40 pounds?

Alphabetical Numbers

Arange all the natural numbers in alphabetical order - which number comes second?

Strange Dice

Number the faces of the cubes to make strange dice with a minimum face sum.

Leaving Transumvania

Find where the drone catches up with the ship given their relative speeds.

Rolling Dice

Find a nice method to work out which number on the dice is uppermost after rolling across a chess board.

Sisters Outnumbering Brothers

Work out the total number of children in Rachel's family using the clues about brothers and sisters.

Time and Calendars

How many times in a 24 hour period do all four digits on my bedside clock change at the same time?

Santa's Small Window

How do you increase the area of a window without changing its height or width?

How Much Richer?

A puzzle about the relative wealth of Maureen compared to Doreen.

Factor Shopping

Find the prices of the items bought if they are different and all factors of the total bill.

Splitting Ten for a Product

Which of the many ways of splitting ten gives the largest product?

Where's the Father

What seems like a familiar puzzle has an unusual twist.

A Frobenius coin problem

What is the largest amount that cannot be made with 5p and 7p coins?

Bus Fare Premonition

How did the bus driver know how much to charge Mrs P and Mrs Q?

A Half Mean Angle

Find the size of the angle at A if it is half of the mean of the angles at B and C.

Food Inflation

The cost of a meal increases by 4% to a whole number of pounds.

Chris and his Unpredictable Kids

A think of a number puzzle with an unpredictable element.

Keith and Kath

Find the ages of Keith and Kath from the clues given.

Two-Faced and Blue

How many of the smaller cubes that make up the 3x3 cube have two faces painted blue?

Santa is Cool

What temperature is reported using the same number in Celsius and Fahrenheit?

Three Trios of Triplets Thrice

A simple question that seventy two percent of a group of people got wrong.

Trains Together

How far apart will the trains be half an hour before they meet?

Six Ropes

Can the pirates win their freedom by tying the six pieces of rope into one large loop?

Bogdan and Wally

In what order should you play Ultimate Noughts and Crosses against Wally and Bogdan?

What's My Name Riddle

Work out the name from the rhyming riddles.

Mathematical Days

What is the date of the next Pythagorean Theorem Day?

Eva's Eggs and Fickle Fractions

How many eggs did Eva take to market in order to make those strange half sales?

Feeding Fools and Horses

How long will the horse feed last the horses after some of them left the stables?

Balancing Balloons

How many balloons must Jamie give to Ben to balance the balloon equation?

A Puzzle from Carl

Carl's puzzle is about the result of dividing the product of his parents' ages by double his own age.

Odds from evens up to 2020

Subract the sum of the odd numbers less than 2020 from the sum of the even numbers less than 2020.

Noel in Lapland

Work out the length of Noel's trip to Lapland given the details of the weather conditions.

Multiple Remainders

What is the second smallest number such that when it is divided by 5 the remainder is 4, and when divided by 7 the remainder is 6?

Coaches to Cambridge

Can you figure out which coach I travelled in when I went to Cambridge?

Percy Cod's Kids

Percy Cod was talking about his children. Can you work out their ages given the ratios?

Carrot-eating Critters

Work out how many of each kind of animal are in the field from their carrot-eating habits.

Red Arrow Square

What fraction of the square does the red arrow cover?

Patsy Loves Percy

The strange case of Percy who seems to be getting older very quickly

Monkeys, Kittens and Dogs

Who is most likely to be able to work out the square root of 121?

Feed The Horses

How long will the remaining feed last the horses that have not been sold?

Strange Addition

If I start at five and add six I get eleven but if I start at six and add seven I get one.

Prime Permutations

Of all the permutations of 1 to 9 used to make nine-digit numbers, how many are prime?

4-Digit Hotel Room Safe Code

Can you work out what number I used to lock and unlock my hotel room safe?

Choir Eye Colour

Figure out the percentage of choir members that do not have blue eyes from the clues given.

Calculator Keys at the Corners of a Rectangle

A question about the four keys at the corners of a rectangle on a calculator.

Average House Numbers

Work out the house numbers from the clues about the mean, median and mode.

Clock in the Mirror

What time was the clock in the mirror really showing?

Delightfully Divisible

Find a pandigital number that is delightfully divisible.

Five integers with a product of 12

Can you find five integers that multiply together to give twelve?

Square in a Rectangle

What is the largest square that can be drawn in the corner of a 10cm by 15cm rectangle?

London Marathon

A question about the average speed required for the second half of the marathon.

Cutting the Lawn

Aynuk and Ayli cut half of the lawn each. How long is each side of the square lawn?

The Missing Pound's Found

A really wonderful answer to the missing pound puzzle.

Forty Five in Four Parts

Split the number 45 into four parts according to the given information.

Shrivelled Spuds

Work out the weight of the potatoes after they have been left out in the sun to dry.

Transposition Error

Work out the bank balance given information about the transposition error.

Counting Sheep

Work out the number of sheep owned by Percy and Patsy from the given clues.

Juggling with Egg Timers

Can you time exactly nine minutes using the four and seven minute egg timers?

Permutation Sum

What is sum of all the four digit numbers containing all of the digits one to four?

Odd Probability

What is the probability that two random numbers are both even if they are not both odd?

Regions in Circles

Calculate the number of regions in a circle formed by intersecting chords.

Brothers and Sisters

Can you work out the number of children in the Numlove family given the clues about brothers and sisters?

Exam Average

What mark is required in the last exam to achieve an 80% overall average?

Cake Cut

Where should the last slice of cake be cut to give two equal pieces?

Holy Sphere

Calculate the remaining volume of the sphere after a cylindrical hole has been drilled through the centre

Jumping Flea

How many different places could the flea find itself after 8 foot-long jumps either north, south, east or west?

Last Digit

How many positive two-digit numbers are there whose square and cube both end in the same digit?

Central Station

The probability that the next train to leave will be going north is five times the probability that the next train to leave will be going south.

Canteen Queue

Is it possible to answer the question if Betsy's age is not known?

Separated Twins

Work out the combination of the safe given the clues about pairs of numbers.

Divisible By Three

A puzzle about two digit numbers that can be made from ten different digits.

Letters In Numbers

A brand new puzzle involving the letters in numbers when written as words.

Square Angled Triangle

The angles of a triangle are all square numbers. What are they?

Tri-Junction Puzzle

What is the probability of the three cars arriving at the road junction not being involved in an accident?

Two Prime Squares

What is the smallest square number (greater than one) that cannot be expressed as the sum of two prime numbers?

The Missing Pound

Where did the missing pound go in this story about three people visiting a restaurant?

Ticks, Tocks, Tacks and Tucks

Find how ticks compare to tocks, tacks and tucks from the given information.

The Power of Christmas

A question about indices to get you thinking mathematically at this festive time of year.

Ant and Dec

What single question could Dec ask Ant to find out what he is thinking?


How far does the bookworm travel on its meal-time journey?

Three Mathematicians

How can the third mathematician be so certain that everyone wants a drink?

Unfinished Game

If the coin tossing game was cut short how would you share the winnings?


Questions about the letters used to make the natural numbers.

Best Dice

Which of the unusual dice would you choose to give you the best chance of winning the prize?

The Birthday Problem

What is the probability of two or more pupils in a class having the same birthday?

Enigma Vowels

A coding question inspired by the film The Imitation Game.

Biased Coin

A mathematical question asked by Microsoft and Google interviewers.

Twelve Days of Christmas

Can you figure out exactly how many gifts the true love sends during the twelve days of the Christmas holiday?

Chased by a Bear

A puzzle about an explorer being chased by a bear along with a question about imperial and metric measures with Measurement Man

Halloween Bases

A puzzle about Why is halloween like Christmas along with news of the new Number Skills Inventory

Torch Tunnel

A puzzle about four people making their way through a tunnel with just one torch along with news of the new numerology page

Cube in Milk

A puzzle about a cube being lowered into a bucket of milk along with news of the new shunting puzzles

The following puzzles are the Transum Advanced Starters.

Airport Security

The old lady has a misconception about conditional probability

Algebraic Product

Finding the value of the expression is easier than you think!

Angle Thinking

Find the range of possible angles, x, for which tan x > cos x > sin x

Average Cycling Speed

Work out the average speed of two journeys. The obvious answer is not the correct answer.

Back To The Factory

Find all the numbers below 1000 which have exactly 20 factors


A misleading way of stating the answer to a simple calculation.

Bertrand's Box Paradox

Bertrand's box paradox is a paradox of elementary probability theory, first posed by Joseph Bertrand in 1889

Best Dice

Which of the unusual dice would you choose to give you the best chance of winning the prize?

Biased Coin

Use a biased coin to obtain a fair result

Car Inequalities

Solve three simultaneous inequalities to find how many cars I own.

Catering for a Function

Find f(x) given f(x-1).

Charging Rhinos

Find the easy way to solve this kinematics problem involving a fly and two rhinos.

Cheryl's Birthday

Use a process of elimination to work out the correct date from the clues given.

Coordinate Distance

Find k given that(-2,k) is 13 units away from (10,9)

Cos 10 Equals p

Find the trigonometric values in terms of the given value, p.


Find the dimensions of a cuboid matching the description given

Curved Angles

How many right angles are there in a semicircle?

Difference Cipher

Find the mathematical word from the cipher

Divisible by 11

Can you prove that a three digit number whose first and third digits add up to the value of the second digit must be divisible by eleven?

Double or Half?

At ten percent change per day is doubling achieved faster than halving?

Eight to the Unknown

Solve the equation using the laws of indices

Exceeds by 99

Find the number whose double exceeds its half by exactly 99.

Exponential Trigonometry

Find, in degrees, all eight of the solutions to the given exponential, trigonometric equation

Fence Optimisation

Find the length of a rectangle enclosing the largest possible area.

Fermi Problem

The classic Fermi problem using standard estimation techniques

Find The Radius

Find the radius of the circle from the small amount of information provided.

Four Fraction Division

Explain why the answer to a series of fraction divisions is a whole number.

GDC Challenge

Produce the given graph on a graphic display calculator

Geometry Snack

Find the value of the marked angle in this diagram from the book Geometry Snacks

Ghosts or Papua New Guinea

A probability prediction based on a biased sample


How far would grandma have travelled after a suitably large number of days given her walking regime?

Hands Together

The hands of a clock are together at midnight. At what time are they next together?

HCF and LCM given

If given the HCF, LCM can you find the numbers?

How Many Left Handers?

Work out the number of members if the probability of left-handed members being randomly selected is given.

Hundred and Fifty Percent

Divide 110 into two parts so that the larger part is 150% of the smaller part.

Index Equation

Solve x squared equals sixteen to the power of x

Is it a Number?

A mathematical object is a number if it ...

Key Eleven

Prove that a four digit number constructed in a certain way will be a multiple of eleven.

Log Perfection

Determine whether the given statements containing logarithms are true or false

Logarithm Equation

Solve an equation containing logarithms with different bases

Maximum Product

Two numbers add up to 10. What's the largest possible product they could have?

Multiple of sum of digits

What number is six times the sum of its digits?

Nine Digit Numbers

How many different nine digit numbers are their that contain each of the digits from one to nine?

Other Child's Gender

What is the probability that the other child is also a boy?

Paper Ratio

Calculate the ratio of the sides of an A4 sheet of paper without any measuring.

Paper Surprising Perimeter

Find the perimeter of a folded sheet of A4 paper as described in this short video.

Parallel Graphs

Determine from their equations which of the straight line graphs are parallel and perpendicular.

Penny Bags

Can you place 63 pennies in bags in such a way that you can give away any amount of money (from 1p to 63p) by giving a selection of these prepacked bags?

Perennial Rivals

Which football team will be first to win four games?

Permutable Functions

Find pairs of functions that are commutative under composition.

Piece of String

Find where a piece of string should be cut to form a circle and a square of equal areas.

Pizza Slice

A problem which can be solved by considering the areas of a triangle and a sector of a circle.

Product of Indices

Find the product of the unknown indices that feature in two equations

Quad Midpoints

What shape is created when the midpoints of the sides of a quadrilateral are joined together?

Restrained Flea

How many different places could the flea find itself after 8 foot-long jumps either north, south, east or west?

Reverse Connection

Find a general rule for the difference between a two digit number and that same number with the digits reversed.

Rice on a Chess Board

How many grains of rice are on a chess board if each square has twice the number of grains as the previous square.

Rich or Poor?

An interesting outcome of percentage increase and decrease

Road Connections

Design roads to connect four houses that are on the corners of a square, side of length one mile, to minimise the total length of the roads.

Rope Around The World

Imagine a long rope wrapped around Earth's equator - One metre longer than it needs to be.

Same Series Sum

Find an arithmetic series and a geometric series that have the same sum of the first five terms.

Same Three Digits

Find expressions which contain indices and evaluate to numbers containing the same digits.

Seventeen Camels

Explain the mathematics of the classic ninteenth century fraction sharing story.


Simplify an algebraic fraction

Singers and Dancers

What fraction of the singers and dancers are both singers and dancers?

Single Fraction

Simplify an expression involving fractions, exponents and a square root.

Sorcerer's Apprentices

The difference between random selection and an 'at least' scenario involving sorcerer's apprentices.

Speed Circles

Find the diameters of the circles in the corners of the square.

Sphere Hole

Find the volume of the remaining part of a sphere after a 10cm cylindrical hole has been drilled through it.

Square in Rectangle

Find the area of a square drawn under the diagonal of a rectangle

Square Root of 1%

What is the square root of one percent?

Tan 22.5

Find an exact value for tan 22.5° without using a calculator.


Find the sum of the tangents of angles on a straight line.

Temperature Sum

Can you explain why 0oC + 0oC does not equal 64oF

Test Scores

Explore the misconception that when adding fractions you add both the numerators and the denominators

Three Right Triangles

Calculate the lengths of the unlabelled sides of these right-angled triangles.

Transum Tonic

What is the largest number of bottles that it is not possible to buy if they come in packs of 6, 9, and 20?


A real life situation that can be analysed with the use of a tree diagram.

Triangle or Quadrilateral

Can a quadrilateral have a straight angle?

Trig Blot

Find all the measurements of the given triangle.

Two Equals One

What is wrong with the algebraic reasoning that shows that 2 = 1 ?

Two Pots

Use tree diagrams to find the surprising result that probabilities of different situations are the same.

Two real numbers

The sum of the reciprocals of two real numbers is -1, and the sum of their cubes is 4. What are they?

Unfinished Game

Share the prize in a fair ratio according to the probability of each player winning.

Uniqueness Starter

Find answers to questions that no one else in the class has thought of.

Unlucky Seven Eleven

Follow the instructions to multiply a chosen number then explain the result you get.

Venn Graphs

Type the equation of a graph into each section of the Venn diagram.

Victorian Times Comparison

Is 10! larger or smaller than the number of seconds in six weeks?

Vowel Code

How many ways can you create a code for the vowels by assigning to each vowel a different vowel?

Weather Reports

Which five different integers multiply together to give 12?

What Question?

Write down all the possible questions that could have been asked if this was the Venn diagram provided in a mathematics exam.

X Divided by 2Y

Why do different calculators not agree on the order of operations?

Zero Even

Prove that zero is an even number.

Eric Levy, United States

Thursday, November 17, 2016

"Thank you for the podcasts! I really enjoy the puzzles. This relates to the 5/29/15 podcast re: coin flipping game that was stopped before completion. The flips when stopped were two Heads and one Tail. You indicate that the options on next 2 tosses are HH, TH, HT, and TT. Since the game stops when one person reaches 3 points, wouldn't HH and HT be the same, as the second flip isn't needed? This seems to match your ultimate answer of 75% and 25%, though ... with the person with Tails only winning with TT, which is 25% chance. I get the same answer but intermediate steps differ. Am I looking at this incorrectly? Thanks!."


Thursday, November 17, 2016

"Dear Eric, Thanks so much for your observations and you are completely right. The only reason I chose to list the next two outcomes was to produce equally likely outcomes making the arithmetic very slightly easier. I am glad you enjoy the puzzles."

Dubai English Speaking School, Twitter

Wednesday, January 24, 2018

Elena Bezoari, Twitter

Saturday, June 8, 2019

Ann, London

Tuesday, September 3, 2019

"Hi there!
Great maths puzzles & activities. Thank you.
Do you have the answers?

[Transum: Hello Ann, Thanks for leaving a comment on the Transum Puzzles page. Yes, each of the puzzles has an answer that appears when you are logged in as a subscriber. You can find a subscription application form here. "

Mike Park, United States

Saturday, October 2, 2021

"I must commend you on nurturing such a thorough and ingenious website of math problems. You offer great exercises, puzzles, review material, and so much more. I really enjoyed using Transum Math."

Whitney Edmondson, Linkedin

Wednesday, March 29, 2023

"This month we ran our puzzle and problem solving team competition amongst the different grades. We decided to improve from the traditional "hard maths" questions and have inquiry and thinking stations. This wasn't about who was the best at just Maths, it was about who was the best at doing Maths using all the MYP ATL Skills.

Thanks again to the fantastic site for the puzzles I used to create the stations. To mention a few brilliant aspects about using this site for Maths stations.

On refreshing you get a new but similar puzzle, points are often generated, instructions included for staff to read and creative interactive levels you can adjust depending on the grade...Completely FREE!"

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.


©1997-2024 WWW.TRANSUM.ORG