Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

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?

Starting with the number 180, take away 9 again and again, joining up the dots as you go. Watch out - don't join all the dots!

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

If you have only four weights, where could you place them in order to balance this equaliser?

Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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

Imagine a pyramid which is built in square layers of small cubes. If we number the cubes from the top, starting with 1, can you picture which cubes are directly below this first cube?

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?

Can you put plus signs in so this is true? 1 2 3 4 5 6 7 8 9 = 99 How many ways can you do it?

You have two egg timers. One takes 4 minutes exactly to empty and the other takes 7 minutes. What times in whole minutes can you measure and how?

This problem is based on the story of the Pied Piper of Hamelin. Investigate the different numbers of people and rats there could have been if you know how many legs there are altogether!

Zumf makes spectacles for the residents of the planet Zargon, who have either 3 eyes or 4 eyes. How many lenses will Zumf need to make all the different orders for 9 families?

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?

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

Can you each work out the number on your card? What do you notice? How could you sort the cards?

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

How have the numbers been placed in this Carroll diagram? Which labels would you put on each row and column?

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.

Here is a chance to play a version of the classic Countdown Game.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

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

This magic square has operations written in it, to make it into a maze. Start wherever you like, go through every cell and go out a total of 15!

Arrange eight of the numbers between 1 and 9 in the Polo Square below so that each side adds to the same total.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Can you arrange 5 different digits (from 0 - 9) in the cross in the way described?

In a Magic Square all the rows, columns and diagonals add to the 'Magic Constant'. How would you change the magic constant of this square?

Got It game for an adult and child. How can you play so that you know you will always win?

Winifred Wytsh bought a box each of jelly babies, milk jelly bears, yellow jelly bees and jelly belly beans. In how many different ways could she make a jolly jelly feast with 32 legs?

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

You have 5 darts and your target score is 44. How many different ways could you score 44?

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

This task follows on from Build it Up and takes the ideas into three dimensions!

Can you find all the ways to get 15 at the top of this triangle of numbers?

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

There are 4 jugs which hold 9 litres, 7 litres, 4 litres and 2 litres. Find a way to pour 9 litres of drink from one jug to another until you are left with exactly 3 litres in three of the jugs.

Cherri, Saxon, Mel and Paul are friends. They are all different ages. Can you find out the age of each friend using the information?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Use your logical-thinking skills to deduce how much Dan's crisps and ice-cream cost altogether.

A game for 2 players. Practises subtraction or other maths operations knowledge.

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

Write the numbers up to 64 in an interesting way so that the shape they make at the end is interesting, different, more exciting ... than just a square.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

Have a go at this game which involves throwing two dice and adding their totals. Where should you place your counters to be more likely to win?

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?

A game for 2 or more players with a pack of cards. Practise your skills of addition, subtraction, multiplication and division to hit the target score.

A group of children are using measuring cylinders but they lose the labels. Can you help relabel them?