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.

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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

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?

The idea of this game is to add or subtract the two numbers on the dice and cover the result on the grid, trying to get a line of three. Are there some numbers that are good to aim for?

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

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?

My briefcase has a three-number combination lock, but I have forgotten the combination. I remember that there's a 3, a 5 and an 8. How many possible combinations are there to try?

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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?

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?

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.

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

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?

Find out what a "fault-free" rectangle is and try to make some of your own.

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?

Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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

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

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

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?

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

If these elves wear a different outfit every day for as many days as possible, how many days can their fun last?

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?

A Sudoku with clues given as sums of entries.

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

Use the clues to work out which cities Mohamed, Sheng, Tanya and Bharat live in.

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?

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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

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 find out in which order the children are standing in this line?

Use the information to describe these marbles. What colours must be on marbles that sparkle when rolling but are dark inside?

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

How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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 10 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.

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?

How many different shapes can you make by putting four right- angled isosceles triangles together?

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?

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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

This challenge is about finding the difference between numbers which have the same tens digit.

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

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?

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

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

Make a pair of cubes that can be moved to show all the days of the month from the 1st to the 31st.