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?

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

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.

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.

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?

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

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

A Sudoku with clues given as sums of entries.

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.

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?

In a square in which the houses are evenly spaced, numbers 3 and 10 are opposite each other. What is the smallest and what is the largest possible number of houses in the square?

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.

Exactly 195 digits have been used to number the pages in a book. How many pages does the book have?

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

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.

Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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.

Here are some rods that are different colours. How could I make a dark green rod using yellow and white rods?

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?

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

You have 4 red and 5 blue counters. How many ways can they be placed on a 3 by 3 grid so that all the rows columns and diagonals have an even number of red counters?

Hover your mouse over the counters to see which ones will be removed. Click to remover them. The winner is the last one to remove a counter. How you can make sure you win?

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.

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?

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

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

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

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?

What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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

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

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

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.

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

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

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

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

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?

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?

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?

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

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

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 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?

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

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

A tetromino is made up of four squares joined edge to edge. Can this tetromino, together with 15 copies of itself, be used to cover an eight by eight chessboard?