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

Make one big triangle so the numbers that touch on the small triangles add to 10.

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?

There are three versions of this challenge. The idea is to change the colour of all the spots on the grid. Can you do it in fewer throws of the dice?

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

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?

Place the numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

There are three baskets, a brown one, a red one and a pink one, holding a total of 10 eggs. Can you use the information given to find out how many eggs are in each basket?

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

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

Can you make a 3x3 cube with these shapes made from small cubes?

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

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.

Use the three triangles to fill these outline shapes. Perhaps you can create some of your own shapes for a friend to fill?

Can you find a path from a number at the top of this network to the bottom which goes through each number from 1 to 9 once and once only?

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.

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?

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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).

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.

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?

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

Place the digits 1 to 9 into the circles so that each side of the triangle adds to the same total.

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

There were chews for 2p, mini eggs for 3p, Chocko bars for 5p and lollypops for 7p in the sweet shop. What could each of the children buy with their money?

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

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?

How many starfish could there be on the beach, and how many children, if I can see 28 arms?

Use these four dominoes to make a square that has the same number of dots on each side.

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

Pat counts her sweets in different groups and both times she has some left over. How many sweets could she have had?

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?

As you come down the ladders of the Tall Tower you collect useful spells. Which way should you go to collect the most spells?

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

Arrange the numbers 1 to 6 in each set of circles below. The sum of each side of the triangle should equal the number in its centre.

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?

You have a set of the digits from 0 – 9. Can you arrange these in the five boxes to make two-digit numbers as close to the targets as possible?

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

What do you notice about these squares of numbers? What is the same? What is different?

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?

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

Sam sets up displays of cat food in his shop in triangular stacks. If Felix buys some, then how can Sam arrange the remaining cans in triangular stacks?

Woof is a big dog. Yap is a little dog. Emma has 16 dog biscuits to give to the two dogs. She gave Woof 4 more biscuits than Yap. How many biscuits did each dog get?

Can you arrange fifteen dominoes so that all the touching domino pieces add to 6 and the ends join up? Can you make all the joins add to 7?

The clockmaker's wife cut up his birthday cake to look like a clock face. Can you work out who received each piece?

In this problem you have to place four by four magic squares on the faces of a cube so that along each edge of the cube the numbers match.

On a farm there were some hens and sheep. Altogether there were 8 heads and 22 feet. How many hens were there?

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

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