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 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?

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

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

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

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?

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

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?

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

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

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

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

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.

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

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

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

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

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

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

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.

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?

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

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?

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?

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

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.

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

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

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?

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?

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?

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.

Katie had a pack of 20 cards numbered from 1 to 20. She arranged the cards into 6 unequal piles where each pile added to the same total. What was the total and how could this be done?

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).

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

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.

Amy's mum had given her £2.50 to spend. She bought four times as many pens as pencils and was given 40p change. How many of each did she buy?

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

Exploring balance and centres of mass can be great fun. The resulting structures can seem impossible. Here are some images to encourage you to experiment with non-breakable objects of your own.

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

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

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.

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?

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?

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?

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.

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?

If these balls are put on a line with each ball touching the one in front and the one behind, which arrangement makes the shortest line of balls?