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?

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

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

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

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

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

Can you find all the different ways of lining up these Cuisenaire rods?

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

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?

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

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

Can you put the numbers from 1 to 15 on the circles so that no consecutive numbers lie anywhere along a continuous straight line?

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

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?

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

Play this well-known game against the computer where each player is equally likely to choose scissors, paper or rock. Why not try the variations too?

How many right angles can you make using two sticks?

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?

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

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?

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

An interactive activity for one to experiment with a tricky tessellation

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

Use the interactivity to make this Islamic star and cross design. Can you produce a tessellation of regular octagons with two different types of triangle?

A game for two people that can be played with pencils and paper. Combine your knowledge of coordinates with some strategic thinking.

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

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

What are the coordinates of the coloured dots that mark out the tangram? Try changing the position of the origin. What happens to the coordinates now?

In your bank, you have three types of coins. The number of spots shows how much they are worth. Can you choose coins to exchange with the groups given to make the same total?

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....?

If you hang two weights on one side of this balance, in how many different ways can you hang three weights on the other side for it to be balanced?

Work out the fractions to match the cards with the same amount of money.

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

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

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.

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

Choose 13 spots on the grid. Can you work out the scoring system? What is the maximum possible score?

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

These interactive dominoes can be dragged around the screen.

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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

Move just three of the circles so that the triangle faces in the opposite direction.