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

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?

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.

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?

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?

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

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.

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

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

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?

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?

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

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?

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

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?

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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?

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

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

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

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

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

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?

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

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?

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

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

Seven friends went to a fun fair with lots of scary rides. They decided to pair up for rides until each friend had ridden once with each of the others. What was the total number rides?

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.

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

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

In this challenge, buckets come in five different sizes. If you choose some buckets, can you investigate the different ways in which they can be filled?

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. . . .

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....?

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?

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

If we had 16 light bars which digital numbers could we make? How will you know you've found them all?

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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

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?

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?