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

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 remover them. The winner is the last one to remove a counter. How you can make sure you win?

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

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....?

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

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?

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?

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?

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

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?

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

How many shapes can you build from three red and two green cubes? Can you use what you've found out to predict the number for four red and two green?

Imagine that the puzzle pieces of a jigsaw are roughly a rectangular shape and all the same size. How many different puzzle pieces could there be?

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

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

Use the clues to find out who's who in the family, to fill in the family tree and to find out which of the family members are mathematicians and which are not.

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?

How many models can you find which obey these rules?

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

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

My coat has three buttons. How many ways can you find to do up all the buttons?

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

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?

Place eight dots on this diagram, so that there are only two dots on each straight line and only two dots on each circle.

Put 10 counters in a row. Find a way to arrange the counters into five pairs, evenly spaced in a row, in just 5 moves, using the rules.

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

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

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

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?

Place eight queens on an chessboard (an 8 by 8 grid) so that none can capture any of the others.

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

You cannot choose a selection of ice cream flavours that includes totally what someone has already chosen. Have a go and find all the different ways in which seven children can have ice cream.

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

When newspaper pages get separated at home we have to try to sort them out and get things in the correct order. How many ways can we arrange these pages so that the numbering may be different?

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?

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?

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 different ways you could split up these rooms so that you have double the number.

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

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

In how many ways can you stack these rods, following the rules?

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?