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.

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

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?

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

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?

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.

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

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?

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?

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

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

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.

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

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

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

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

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?

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 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.

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

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?

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

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?

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 article for teachers suggests activities based on pegboards, from pattern generation to finding all possible triangles, for example.

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

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

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

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 ...?

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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?

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

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

How many trains can you make which are the same length as Matt's, using rods that are identical?

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

Use these head, body and leg pieces to make Robot Monsters which are different heights.

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

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

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