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 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?

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.

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?

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.

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.

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?

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

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

The Red Express Train usually has five red carriages. How many ways can you find to add two blue carriages?

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?

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?

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. . . .

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

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

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?

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?

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

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

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.

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?

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?

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

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

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

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

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

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?

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

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

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

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

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.

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

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.

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

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

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?

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

Can you find which shapes you need to put into the grid to make the totals at the end of each row and the bottom of each column?

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.

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.

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.