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?

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?

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.

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?

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?

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?

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?

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.

Place six toy ladybirds into the box so that there are two ladybirds in every column and every row.

Take three differently coloured blocks - maybe red, yellow and blue. Make a tower using one of each colour. How many different towers can you make?

Try this matching game which will help you recognise different ways of saying the same time interval.

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

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.

This article for primary teachers suggests ways in which to help children become better at working systematically.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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?

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

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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

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

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.

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. . . .

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.

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

In this problem it is not the squares that jump, you do the jumping! The idea is to go round the track in as few jumps as possible.

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

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?

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.

Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.

This challenge extends the Plants investigation so now four or more children are involved.

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

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....?

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

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

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 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?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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

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

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

Can you find all the different triangles on these peg boards, and find their angles?

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

Find all the numbers that can be made by adding the dots on two dice.

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

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

An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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?

Can you fill in the empty boxes in the grid with the right shape and colour?

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.