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.

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?

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?

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?

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.

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

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

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.

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).

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

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?

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?

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

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

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

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

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?

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?

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

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

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

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

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

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

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?

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?

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

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

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 go from A to Z right through the alphabet in the hexagonal maze?

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?

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

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.

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

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?

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

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.

In 1871 a mathematician called Augustus De Morgan died. De Morgan made a puzzling statement about his age. Can you discover which year De Morgan was born in?

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

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

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

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?

Use the information about Sally and her brother to find out how many children there are in the Brown family.

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?

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?

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

Use five steps to count forwards or backwards in 1s or 10s to get to 50. What strategies did you use?

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?

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?