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

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

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?

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

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?

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

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

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

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

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?

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

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

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

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?

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?

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

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

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?

Can you work out how to balance this equaliser? You can put more than one weight on a hook.

Use your mouse to move the red and green parts of this disc. Can you make images which show the turnings described?

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

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

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

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?

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

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

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?

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.

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

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?

Terry and Ali are playing a game with three balls. Is it fair that Terry wins when the middle ball is red?

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.

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Can you find all the different triangles on these peg boards, and find their angles?

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

Find out how we can describe the "symmetries" of this triangle and investigate some combinations of rotating and flipping it.

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

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

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

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

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?

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

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

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