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?

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?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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

Arrange any number of counters from these 18 on the grid to make a rectangle. What numbers of counters make rectangles? How many different rectangles can you make with each number of counters?

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

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

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

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

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

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

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

Choose the size of your pegboard and the shapes you can make. Can you work out the strategies needed to block your opponent?

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

This activity challenges you to make collections of shapes. Can you give your collection a name?

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

What happens when you try and fit the triomino pieces into these two grids?

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?

Cut four triangles from a square as shown in the picture. How many different shapes can you make by fitting the four triangles back together?

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

What shape is the overlap when you slide one of these shapes half way across another? Can you picture it in your head? Use the interactivity to check your visualisation.

In this activity, the computer chooses a times table and shifts it. Can you work out the table and the shift each time?

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

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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?

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

A game for two people, or play online. Given a target number, say 23, and a range of numbers to choose from, say 1-4, players take it in turns to add to the running total to hit their target.

What is the greatest number of squares you can make by overlapping three squares?

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

A game to be played against the computer, or in groups. Pick a 7-digit number. A random digit is generated. What must you subract to remove the digit from your number? the first to zero wins.

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. . . .

An interactive activity for one to experiment with a tricky tessellation

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

A game in which players take it in turns to choose a number. Can you block your opponent?

A game for 2 players that can be played online. Players take it in turns to select a word from the 9 words given. The aim is to select all the occurrences of the same letter.

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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

Train game for an adult and child. Who will be the first to make the train?

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

Calculate the fractional amounts of money to match pairs of cards with the same value.

Here are some rods that are different colours. How could I make a yellow rod using white and red rods?

Try out the lottery that is played in a far-away land. What is the chance of winning?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

A train building game for two players. Can you be the one to complete the train?

Investigate which numbers make these lights come on. What is the smallest number you can find that lights up all the lights?

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

How many trains can you make which are the same length as Matt's and Katie's, using rods that are identical?