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

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

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.

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?

There are seven pots of plants in a greenhouse. They have lost their labels. Perhaps you can help re-label them.

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

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

There is a long tradition of creating mazes throughout history and across the world. This article gives details of mazes you can visit and those that you can tackle on paper.

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

Can you make a train the same length as Laura's but using three differently coloured rods? Is there only one way of doing it?

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 package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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

The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

Can you order the digits from 1-3 to make a number which is divisible by 3 so when the last digit is removed it becomes a 2-figure number divisible by 2, and so on?

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?

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?

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?

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.

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

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.

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?

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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.

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

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?

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

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

Can you find the chosen number from the grid using the clues?

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?

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 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?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

Investigate the different ways you could split up these rooms so that you have double the number.

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

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has 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?

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.