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

If each of these three shapes has a value, can you find the totals of the combinations? Perhaps you can use the shapes to make the given totals?

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?

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

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

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

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

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

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

Using 3 rods of integer lengths, none longer than 10 units and not using any rod more than once, you can measure all the lengths in whole units from 1 to 10 units. How many ways can you do this?

Fill in the numbers to make the sum of each row, column and diagonal equal to 34. For an extra challenge try the huge American Flag magic square.

A game for 2 people using a pack of cards Turn over 2 cards and try to make an odd number or a multiple of 3.

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?

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?

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!

The picture shows a lighthouse and many underwater creatures. If you know the markings on the lighthouse are 1m apart, can you work out the distances between some of the different creatures?

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

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

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?

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?

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

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

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?

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

Try adding together the dates of all the days in one week. Now multiply the first date by 7 and add 21. Can you explain what happens?

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

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

A lady has a steel rod and a wooden pole and she knows the length of each. How can she measure out an 8 unit piece of pole?

Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?

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?

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?

Vera is shopping at a market with these coins in her purse. Which things could she give exactly the right amount for?

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

Lolla bought a balloon at the circus. She gave the clown six coins to pay for it. What could Lolla have paid for the balloon?

Cassandra, David and Lachlan are brothers and sisters. They range in age between 1 year and 14 years. Can you figure out their exact ages from the clues?

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

Ten cards are put into five envelopes so that there are two cards in each envelope. The sum of the numbers inside it is written on each envelope. What numbers could be inside the envelopes?

We start with one yellow cube and build around it to make a 3x3x3 cube with red cubes. Then we build around that red cube with blue cubes and so on. How many cubes of each colour have we used?

Add the sum of the squares of four numbers between 10 and 20 to the sum of the squares of three numbers less than 6 to make the square of another, larger, number.

Arrange three 1s, three 2s and three 3s in this square so that every row, column and diagonal adds to the same total.

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.