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

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

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

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?

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.

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?

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?

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?

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.

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

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?

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

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.

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?

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?

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

In the planet system of Octa the planets are arranged in the shape of an octahedron. How many different routes could be taken to get from Planet A to Planet Zargon?

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.

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

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?

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

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

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

How could you put eight beanbags in the hoops so that there are four in the blue hoop, five in the red and six in the yellow? Can you find all the ways of doing this?

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

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?

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?

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

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?

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?

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.

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.

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

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

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. . . .

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?

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

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 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?

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

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?