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?

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?

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

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.

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

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

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

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

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

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).

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

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

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

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?

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?

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 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?

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

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?

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

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

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?

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

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.

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?

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

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?

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

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?

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.

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

All the girls would like a puzzle each for Christmas and all the boys would like a book each. Solve the riddle to find out how many puzzles and books Santa left.

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

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?

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

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

On the planet Vuv there are two sorts of creatures. The Zios have 3 legs and the Zepts have 7 legs. The great planetary explorer Nico counted 52 legs. How many Zios and how many Zepts were there?

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

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

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?

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.

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

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

Mrs Morgan, the class's teacher, pinned numbers onto the backs of three children. Use the information to find out what the three numbers were.

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?