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.

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.

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.

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?

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.

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?

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?

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.

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 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?

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

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

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

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?

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

A Sudoku with clues given as sums of entries.

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. . . .

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

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

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.

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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?

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?

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

In how many ways could Mrs Beeswax put ten coins into her three puddings so that each pudding ended up with at least two coins?

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

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

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

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?

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?

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

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 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.

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

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.

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

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.

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

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

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?

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

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

A challenging activity focusing on finding all possible ways of stacking rods.

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