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.

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

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

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 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?

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

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?

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.

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

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.

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.

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.

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.

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

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

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?

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

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

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?

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

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

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?

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

Place the numbers 1 to 10 in the circles so that each number is the difference between the two numbers just below it.

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

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

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?

There are to be 6 homes built on a new development site. They could be semi-detached, detached or terraced houses. How many different combinations of these can you find?

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

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?

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

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

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

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

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

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

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Try out the lottery that is played in a far-away land. What is the chance of winning?

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

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?

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?

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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

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

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

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

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