Maths Puzzles

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

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


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