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?

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.

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.

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

A Sudoku with clues given as sums of entries.

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?

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.

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.

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

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

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?

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....?

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

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

This practical challenge invites you to investigate the different squares you can make on a square geoboard or pegboard.

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?

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

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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

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

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

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 the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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

Use the interactivity to find all the different right-angled triangles you can make by just moving one corner of the starting triangle.

What could the half time scores have been in these Olympic hockey matches?

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

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?

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

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

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

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

Investigate all the different squares you can make on this 5 by 5 grid by making your starting side go from the bottom left hand point. Can you find out the areas of all these squares?

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

What is the greatest number of counters you can place on the grid below without four of them lying at the corners of a square?

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

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.

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

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

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?

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

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.

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?

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

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 task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a 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 numbers 1 to 6 in the circles so that each number is the difference between the two numbers just below it.

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