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.

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.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

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?

Add or subtract the two numbers on the spinners and try to complete a row of three. Are there some numbers that are good to aim for?

Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

How will you go about finding all the jigsaw pieces that have one peg and one hole?

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

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.

This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

What is the best way to shunt these carriages so that each train can continue its journey?

10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

Can you shunt the trucks so that the Cattle truck and the Sheep truck change places and the Engine is back on the main line?

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

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.

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

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

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

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

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?

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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.

Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

Design an arrangement of display boards in the school hall which fits the requirements of different people.

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.

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....?

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

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

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

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.

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

Can you find out in which order the children are standing in this line?

Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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?

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

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

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?

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

Chandra, Jane, Terry and Harry ordered their lunches from the sandwich shop. Use the information below to find out who ordered each sandwich.

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

Swap the stars with the moons, using only knights' moves (as on a chess board). What is the smallest number of moves possible?

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?

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

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