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?

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

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

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 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?

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

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

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.

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?

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?

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?

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?

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

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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?

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

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?

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

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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

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

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.

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

How many different triangles can you draw on the dotty grid which each have one dot in the middle?

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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

How can you arrange the 5 cubes so that you need the smallest number of Brush Loads of paint to cover them? Try with other numbers of cubes as well.

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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

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.

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

Building up a simple Celtic knot. Try the interactivity or download the cards or have a go on squared paper.

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.

These practical challenges are all about making a 'tray' and covering it with paper.

How many models can you find which obey these rules?

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

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

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

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?

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

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?

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?

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?

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