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.

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.

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?

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

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?

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.

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.

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

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. . . .

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

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?

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

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

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

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?

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

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

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

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?

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.

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

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

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.

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

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.

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

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.

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

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?

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?

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

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

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

Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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

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.

When intergalactic Wag Worms are born they look just like a cube. Each year they grow another cube in any direction. Find all the shapes that five-year-old Wag Worms can be.

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

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

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?

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

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

Use the interactivity to help get a feel for this problem and to find out all the possible ways the balls could land.

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?