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?

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

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?

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.

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 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.

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.

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

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

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

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

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

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

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

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

A Sudoku with clues given as sums of entries.

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

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

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

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

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?

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

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?

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?

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.

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.

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. . . .

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

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

Find out about Magic Squares in this article written for students. Why are they magic?!

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

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?

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?

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

In a bowl there are 4 Chocolates, 3 Jellies and 5 Mints. Find a way to share the sweets between the three children so they each get the kind they like. Is there more than one way to do it?

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?

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?

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

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

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?

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

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

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?

This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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.