There is a great amount of satisfaction that can be obtained from solving a mathematical puzzle. There is a range of puzzles on this page, all with a mathematical connection, that are just waiting to be solved. You can earn Transum Trophies for the puzzles you solve.
Find all the ways of painting the faces of cubes using only two colours.
Arrange the given digits to make three numbers such that two of them add up to the third.
Use the pieces of the tangram puzzle to make the basic shapes then complete the table showing which shapes are possible.
Turn your calculator upside down to make words out of the answers to these questions.
Vowels have been taken out of mathematical words. Can you recognise them?
If you were to pick up the sticks from this pile so that you were always removing the top stick what calculation would you create?
Arrange the digits one to nine on the spaces provided to make two division calculations containing multiples of three.
Arrange the digits one to nine to make the four calculations correct.
Place the digits one to nine in each of the regions created by the Olympic rings so that the sum of the numbers in each ring is the same.
An extensive collection of Arithmagons arranged in levels according to their features. Find the missing numbers in these online, self-checking exercises and discover the wonders of Arithmagons.
Divide the grid into rectangular pieces so that the area of each piece is the same as the number it contains.
A hands on activity requiring students to arrange Christmas ornaments in a square box.
Find the five numbers which when added or multiplied together in pairs to produce the given sums or products.
Find the path to the centre of the labyrinth by moving along the prime numbers.
Can you arrange the seven counters on the grid despite their truculent behaviour?
An interactive mathematical crossword for you to do online. Find the missing words from the given clues.
Use your knowledge of rectangle areas to calculate the missing measurement of these composite diagrams.
A game, a puzzle and a challenge involving counters being placed at the corners of a square on a grid.
Arrange the scallywags and scoundrels on the chairs so that the numbers of any two sitting next to each other add up to a prime number.
Find which numbers in a given list do not combine with other numbers on the list to make a given sum.
Can you arrange all of the counters on the grid to form 10 lines of three counters?
Arrange the dominoes in seven squares. The number of dots along each side of the square must be equal to the number in the middle
Click on six fleur-de-lis to leave an even number in each row and column.
This is an interactive version of the puzzle described by Henry Ernest Dudeney in The Canterbury Puzzles
Arrange the digits one to nine to make a number which is divisible in the way described.
Use the digits 1 to 9 to make three 3 digit numbers which add up to 999.
Arrange the numbers on the squares so that the totals along each line of three squares are equal.
An interactive activity challenging you to reproduce a pattern of coloured squares according to given clues.
A puzzle requiring the arrangement of numbers on the function machines to link the given input numbers to the correct output.
Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.
A jumbled moving-block puzzle cube is shown as a net. Can you solve it?
Find the hidden wallaby using the clues revealed at the chosen coordinates.
Can you make 4 litres if you only have 7 and 5 litre jugs?
Crack the code by replacing the encrypted letters in the given text. There are lots of hints provided about code breaking techniques.
How many different sets of four dots can be joined to form a square?
Move the pieces of the tower from one place to another in the minimum number of moves.
Arrange the given numbers on the cross so that the sum of the numbers in both diagonals is the same.
A drag and drop activity challenging you to arrange the digits to produce the largest possible product.
A different way to complete a Sudoku puzzle with clues available at every stage.
Arrange numbers on the plane shaped grid to produce the given totals
Fill in the squares according to the clues given by the string of numbers for each row and column.
Numbers in the bricks are found by adding the two bricks immediately below together. Can you achieve the given target?
The chessboard has been broken into 13 pieces. Can you put it back together?
This is quite a challenging number grouping puzzle requiring a knowledge of prime, square and triangular numbers.
The Transum version of the traditional sliding tile puzzle.
Find where the mines are hidden without stepping on one.
Arrange the twelve pentominoes in the outline of a rectangle.
Online, interactive jigsaw puzzles of grids of numbers.
An online interactive jigsaw puzzle of a grid of Roman numerals.
A number arranging puzzle with seven levels of challenge.
Can you get your car out of the very crowded car park by moving other cars forwards or backwards?
Find expressions using only one digit which equal the given targets.
Arrange the numbers from 1 to 9 to make an expression with a value of 100.
Like the magic square but all of the totals should be different.
Each row, column and diagonal should produce the same sum.
Solve the problem of getting four people through a tunnel with one torch in the minimum amount of time.
Can you find a 6 digit number containing two each of the digits one to three which obeys the rules given?
Can you draw these diagrams without lifting your pencil from the paper? This is an interactive version of the traditional puzzle.
The traditional River Crossing challenge. Can you do it in the smallest number of moves?
Arrange the numbers from 1 to 6 in the spaces to make the division calculation correct.
Calculate the areas of all the possible quadrilaterals that can be constructed by joining together dots on this grid.
Make a schedule for the 24-hour Darts Marathon which will keep everyone happy!
Change the numbers on the apples so that the number on the lemon is the given total.
Let the psychic read the cards and reveal which number you have chosen.
Interactive, randomly-generated, number-based logic puzzle designed to develop numeracy skills.
Arrange the numbers from 1 to 14 in the spaces to make the sums correct.
Interactive number-based logic puzzles similar to those featuring in daily newspapers.
A logical challenge requiring a strategy to update each of the numbers in a grid.
Arrange the nine pieces of the puzzle on the grid to make the given polygon.
A counter moving challenge invented in northern Thailand.
Drag the numbers into the red cells so that the sum of the three numbers in each row and each column is a prime number.
Arrange the cards to create a valid mathematical statement.
Find the mathematical words in the grid of letters.
The students numbered 1 to 8 should sit on the chairs so that no two consecutively numbered students sit next to each other.
In how many different ways can the numbers be arranged to give the same totals?
Drag the 20 flowers into the gardens so that 9 flowers are visible from each window of the house.
Join up the stars to find the hidden regular polygons.
Place the nine numbers in the table so they obey the row and column headings.
Use the pieces of the T puzzle to fit into the outlines provided.
Move the trams to their indicated parking places in the shunting yard as quickly as possible.
Find all of the possible ways of making the magic total from the numbers in this four by four magic square.
There are plenty more puzzles on the Transum website.
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?
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.
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?
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?
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?
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
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.
Best Dice
Which of the unusual dice would you choose to give you the best chance of winning the prize?
Cheryl's Birthday
Use a process of elimination to work out the correct date from the clues given.
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?
Fence Optimisation
Find the length of a rectangle enclosing the largest possible area.
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.
Grandmother
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?
How Many Left Handers?
Work out the number of members if the probability of left-handed members being randomly selected is given.
Maximum Product
Two numbers add up to 10. What's the largest possible product they could have?
Nine Digit Numbers
How many different nine digit numbers are their that contain each of the digits from one to nine?
Paper Perimeter
Find the perimeter of a folded sheet of A4 paper as described in this short video.
Paper Ratio
Calculate the ratio of the sides of an A4 sheet of paper without any measuring.
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?
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 considereing the areas of a triangle and a sector of a circle.
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.
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.
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 ex
Sphere Hole
Find the volume of the remaining part of a sphere after a 10cm cylindrical hole has been drilled through it.
Three Right Triangles
Calculate the lengths of the unlabelled sides of these right-angled triangles.
Tri-Junction
A real life situation that can be analysed with the use of a tree diagram.
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 willing.
Unlucky Seven Eleven
Follow the instructions to multiply a chosen number then explain the result you get.
Vowel Code
How many ways can you create a code for the vowels by assigning to each vowel a different vowel?
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.
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!."
Transum,
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