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?

My cube has inky marks on each face. Can you find the route it has taken? What does each face look like?

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?

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?

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

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?

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

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

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

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?

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?

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

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?

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?

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?

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

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?

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

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

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

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

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?

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

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?

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?

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?

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

Start with three pairs of socks. Now mix them up so that no mismatched pair is the same as another mismatched pair. Is there more than one way to do it?

In this town, houses are built with one room for each person. There are some families of seven people living in the town. In how many different ways can they build their houses?

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?

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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?

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

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. . . .

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

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.

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?

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

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.