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

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?

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

Can you hang weights in the right place to make the equaliser balance?

Overlaying pentominoes can produce some effective patterns. Why not use LOGO to try out some of the ideas suggested here?

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!

Make one big triangle so the numbers that touch on the small triangles add to 10. You could use the interactivity to help you.

Choose four of the numbers from 1 to 9 to put in the squares so that the differences between joined squares are odd.

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

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

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

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

Can you make the green spot travel through the tube by moving the yellow spot? Could you draw a tube that both spots would follow?

An interactive game to be played on your own or with friends. Imagine you are having a party. Each person takes it in turns to stand behind the chair where they will get the most chocolate.

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

Can you fit the tangram pieces into the outline of this telephone?

Can you fit the tangram pieces into the outline of Little Fung at the table?

Can you fit the tangram pieces into the outlines of these clocks?

Can you fit the tangram pieces into the outlines of these people?

Can you fit the tangram pieces into the outline of this brazier for roasting chestnuts?

Three beads are threaded on a circular wire and are coloured either red or blue. Can you find all four different combinations?

Square It game for an adult and child. Can you come up with a way of always winning this game?

Players take it in turns to choose a dot on the grid. The winner is the first to have four dots that can be joined to form a square.

If you can post the triangle with either the blue or yellow colour face up, how many ways can it be posted altogether?

Yasmin and Zach have some bears to share. Which numbers of bears can they share so that there are none left over?

How many triangles can you make using sticks that are 3cm, 4cm and 5cm long?

Imagine a wheel with different markings painted on it at regular intervals. Can you predict the colour of the 18th mark? The 100th mark?

What shaped overlaps can you make with two circles which are the same size? What shapes are 'left over'? What shapes can you make when the circles are different sizes?

Try to stop your opponent from being able to split the piles of counters into unequal numbers. Can you find a strategy?

Can you fit the tangram pieces into the outline of the child walking home from school?

Can you fit the tangram pieces into the outlines of the chairs?

Incey Wincey Spider game for an adult and child. Will Incey get to the top of the drainpipe?

An interactive activity for one to experiment with a tricky tessellation

A game for 1 person. Can you work out how the dice must be rolled from the start position to the finish? Play on line.

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Exchange the positions of the two sets of counters in the least possible number of moves

How many times in twelve hours do the hands of a clock form a right angle? Use the interactivity to check your answers.

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?

A game for 2 people that everybody knows. You can play with a friend or online. If you play correctly you never lose!

How many different rhythms can you make by putting two drums on the wheel?

An interactive game for 1 person. You are given a rectangle with 50 squares on it. Roll the dice to get a percentage between 2 and 100. How many squares is this? Keep going until you get 100. . . .

A shape and space game for 2,3 or 4 players. Be the last person to be able to place a pentomino piece on the playing board. Play with card, or on the computer.

Board Block game for two. Can you stop your partner from being able to make a shape on the board?

The aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

A game for 1 or 2 people. Use the interactive version, or play with friends. Try to round up as many counters as possible.