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

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

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....?

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

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

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

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?

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?

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.

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

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

Ben and his mum are planting garlic. Use the interactivity to help you find out how many cloves of garlic they might have had.

Sort the houses in my street into different groups. Can you do it in any other ways?

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

How many different triangles can you make on a circular pegboard that has nine pegs?

This was a problem for our birthday website. Can you use four of these pieces to form a square? How about making a square with all five pieces?

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?

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?

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

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

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

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

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

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?

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

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

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?

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 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?

Can you fit the tangram pieces into the outlines of the lobster, yacht and cyclist?

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?

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

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

How can the same pieces of the tangram make this bowl before and after it was chipped? Use the interactivity to try and work out what is going on!

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

Investigate how the four L-shapes fit together to make an enlarged L-shape. You could explore this idea with other shapes too.

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

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

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

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

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

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