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.

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

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.

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

An investigation that gives you the opportunity to make and justify predictions.

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?

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

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.

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

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

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

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

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?

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?

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

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

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

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

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

Can you find the chosen number from the grid using the clues?

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

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.

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?

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

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

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

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

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

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

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

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?

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

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

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?

How many different ways can you find to join three equilateral triangles together? Can you convince us that you have found them all?

A merchant brings four bars of gold to a jeweller. How can the jeweller use the scales just twice to identify the lighter, fake bar?

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