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?

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?

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

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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

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

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

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

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

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?

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

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?

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

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

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 can you put five cereal packets together to make different shapes if you must put them face-to-face?

A dog is looking for a good place to bury his bone. Can you work out where he started and ended in each case? What possible routes could he have taken?

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

Using different numbers of sticks, how many different triangles are you able to make? Can you make any rules about the numbers of sticks that make the most triangles?

Are all the possible combinations of two shapes included in this set of 27 cards? How do you know?

If you split the square into these two pieces, it is possible to fit the pieces together again to make a new shape. How many new shapes can you make?

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

When I fold a 0-20 number line, I end up with 'stacks' of numbers on top of each other. These challenges involve varying the length of the number line and investigating the 'stack totals'.

In how many ways can you fit two of these yellow triangles together? Can you predict the number of ways two blue triangles can be fitted together?

What is the smallest cuboid that you can put in this box so that you cannot fit another that's the same into it?

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?

An activity making various patterns with 2 x 1 rectangular tiles.

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 quadrilaterals can be made by joining the dots on the 8-point circle?

Take 5 cubes of one colour and 2 of another colour. How many different ways can you join them if the 5 must touch the table and the 2 must not touch the table?

This problem focuses on Dienes' Logiblocs. What is the same and what is different about these pairs of shapes? Can you describe the shapes in the picture?

Let's say you can only use two different lengths - 2 units and 4 units. Using just these 2 lengths as the edges how many different cuboids can you make?

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

Find your way through the grid starting at 2 and following these operations. What number do you end on?

A magician took a suit of thirteen cards and held them in his hand face down. Every card he revealed had the same value as the one he had just finished spelling. How did this work?

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

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

The ancient Egyptians were said to make right-angled triangles using a rope with twelve equal sections divided by knots. What other triangles could you make if you had a rope like this?

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

What is the best way to shunt these carriages so that each train can continue its journey?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

Use the clues about the symmetrical properties of these letters to place them on the grid.