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.

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.

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?

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?

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.

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

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

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?

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?

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?

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?

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

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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

These activities focus on finding all possible solutions so if you work in a systematic way, you won't leave any out.

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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?

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

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

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.

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?

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.

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

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

How many different journeys could you make if you were going to visit four stations in this network? How about if there were five stations? Can you predict the number of journeys for seven stations?

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 train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

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.

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

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

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?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

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.

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

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

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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

Kate has eight multilink cubes. She has two red ones, two yellow, two green and two blue. She wants to fit them together to make a cube so that each colour shows on each face just once.

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....?

Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

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

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

Two children made up a game as they walked along the garden paths. Can you find out their scores? Can you find some paths of your own?

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