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This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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A shunting puzzle for 1 person. Swop the positions of the counters at the top and bottom of the board.

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Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

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A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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Strike it Out game for an adult and child. Can you stop your partner from being able to go?

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Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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Can you use the information to find out which cards I have used?

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Can you beat the computer in the challenging strategy game?

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Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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Put operations signs between the numbers 3 4 5 6 to make the highest possible number and lowest possible number.

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You have two sets of the digits 0 – 9. Can you arrange these in the five boxes to make four-digit numbers as close to the target numbers as possible?

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Using only six straight cuts, find a way to make as many pieces of pizza as possible. (The pieces can be different sizes and shapes).

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Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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Can you make a cycle of pairs that add to make a square number using all the numbers in the box below, once and once only?

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Using some or all of the operations of addition, subtraction, multiplication and division and using the digits 3, 3, 8 and 8 each once and only once make an expression equal to 24.

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Use the 'double-3 down' dominoes to make a square so that each side has eight dots.

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Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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Fill in the missing numbers so that adding each pair of corner numbers gives you the number between them (in the box).

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If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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Throughout these challenges, the touching faces of any adjacent dice must have the same number. Can you find a way of making the total on the top come to each number from 11 to 18 inclusive?

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There are 44 people coming to a dinner party. There are 15 square tables that seat 4 people. Find a way to seat the 44 people using all 15 tables, with no empty places.

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Can you see how these factor-multiple chains work? Find the chain which contains the smallest possible numbers. How about the largest possible numbers?

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Nine squares with side lengths 1, 4, 7, 8, 9, 10, 14, 15, and 18 cm can be fitted together to form a rectangle. What are the dimensions of the rectangle?

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Can you find a reliable strategy for choosing coordinates that will locate the treasure in the minimum number of guesses?

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One quarter of these coins are heads but when I turn over two coins, one third are heads. How many coins are there?

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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

A cinema has 100 seats. Is it possible to fill every seat and take exactly £100?

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Using the statements, can you work out how many of each type of rabbit there are in these pens?

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Skippy and Anna are locked in a room in a large castle. The key to that room, and all the other rooms, is a number. The numbers are locked away in a problem. Can you help them to get out?

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Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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There are 78 prisoners in a square cell block of twelve cells. The clever prison warder arranged them so there were 25 along each wall of the prison block. How did he do it?

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56 406 is the product of two consecutive numbers. What are these two numbers?

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Find at least one way to put in some operation signs (+ - x ÷) to make these digits come to 100.

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Your challenge is to find the longest way through the network following this rule. You can start and finish anywhere, and with any shape, as long as you follow the correct order.

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Work out Tom's number from the answers he gives his friend. He will only answer 'yes' or 'no'.

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Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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Start by putting one million (1 000 000) into the display of your calculator. Can you reduce this to 7 using just the 7 key and add, subtract, multiply, divide and equals as many times as you like?

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Can you arrange the digits 1,2,3,4,5,6,7,8,9 into three 3-digit numbers such that their total is close to 1500?

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Can you make dice stairs using the rules stated? How do you know you have all the possible stairs?

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Can you draw a continuous line through 16 numbers on this grid so that the total of the numbers you pass through is as high as possible?

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Is it possible to draw a 5-pointed star without taking your pencil off the paper? Is it possible to draw a 6-pointed star in the same way without taking your pen off?

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The discs for this game are kept in a flat square box with a square hole for each. Use the information to find out how many discs of each colour there are in the box.

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Jo has three numbers which she adds together in pairs. When she does this she has three different totals: 11, 17 and 22 What are the three numbers Jo had to start with?”

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What can you say about these shapes? This problem challenges you to create shapes with different areas and perimeters.

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Complete the following expressions so that each one gives a four digit number as the product of two two digit numbers and uses the digits 1 to 8 once and only once.

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Use the numbers in the box below to make the base of a top-heavy pyramid whose top number is 200.

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I was looking at the number plate of a car parked outside. Using my special code S208VBJ adds to 65. Can you crack my code and use it to find out what both of these number plates add up to?

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Using the numbers 1, 2, 3, 4 and 5 once and only once, and the operations x and ÷ once and only once, what is the smallest whole number you can make?