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.

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?

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.

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

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?

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

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?

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?!

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

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

A Sudoku with clues given as sums of entries.

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.

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

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.

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

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.

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.

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?

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

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

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?

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

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

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

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

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

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.

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

Sitting around a table are three girls and three boys. Use the clues to work out were each person is sitting.

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

The Vikings communicated in writing by making simple scratches on wood or stones called runes. Can you work out how their code works using the table of the alphabet?

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?

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?

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

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

These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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

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

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

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

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?

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

If you put three beads onto a tens/ones abacus you could make the numbers 3, 30, 12 or 21. What numbers can be made with six beads?

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?

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