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?

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?

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

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?

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?

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

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

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?

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

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

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

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?

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

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?

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

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

The challenge here is to find as many routes as you can for a fence to go so that this town is divided up into two halves, each with 8 blocks.

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

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

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

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?

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.

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.

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

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?

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 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?

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.

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

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

In this matching game, you have to decide how long different events take.

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?

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

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

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

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

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....?

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. . . .

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

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

If you have three circular objects, you could arrange them so that they are separate, touching, overlapping or inside each other. Can you investigate all the different possibilities?