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 aim of the game is to slide the green square from the top right hand corner to the bottom left hand corner in the least number of moves.

A game for 2 players with similaritlies to NIM. Place one counter on each spot on the games board. Players take it is turns to remove 1 or 2 adjacent counters. The winner picks up the last counter.

An article for teachers and pupils that encourages you to look at the mathematical properties of similar games.

Watch this video to see how to roll the dice. Now it's your turn! What do you notice about the dice numbers you have recorded?

Are these statements relating to odd and even numbers always true, sometimes true or never true?

Can you work out how to win this game of Nim? Does it matter if you go first or second?

Nim-7 game for an adult and child. Who will be the one to take the last counter?

Here are two kinds of spirals for you to explore. What do you notice?

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.

Here are some arrangements of circles. How many circles would I need to make the next size up for each? Can you create your own arrangement and investigate the number of circles it needs?

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

Use the interactivity to investigate what kinds of triangles can be drawn on peg boards with different numbers of pegs.

Can you see why 2 by 2 could be 5? Can you predict what 2 by 10 will be?

Place the numbers from 1 to 9 in the squares below so that the difference between joined squares is odd. How many different ways can you do this?

In this problem we are looking at sets of parallel sticks that cross each other. What is the least number of crossings you can make? And the greatest?

Investigate the sum of the numbers on the top and bottom faces of a line of three dice. What do you notice?

This problem challenges you to find out how many odd numbers there are between pairs of numbers. Can you find a pair of numbers that has four odds between them?

Stop the Clock game for an adult and child. How can you make sure you always win this game?

Find a route from the outside to the inside of this square, stepping on as many tiles as possible.

This activity involves rounding four-digit numbers to the nearest thousand.

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

If there are 3 squares in the ring, can you place three different numbers in them so that their differences are odd? Try with different numbers of squares around the ring. What do you notice?

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

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

This is a game for two players. Can you find out how to be the first to get to 12 o'clock?

Can you dissect an equilateral triangle into 6 smaller ones? What number of smaller equilateral triangles is it NOT possible to dissect a larger equilateral triangle into?

Four bags contain a large number of 1s, 3s, 5s and 7s. Pick any ten numbers from the bags above so that their total is 37.

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.

Watch this film carefully. Can you find a general rule for explaining when the dot will be this same distance from the horizontal axis?

One block is needed to make an up-and-down staircase, with one step up and one step down. How many blocks would be needed to build an up-and-down staircase with 5 steps up and 5 steps down?

Put the numbers 1, 2, 3, 4, 5, 6 into the squares so that the numbers on each circle add up to the same amount. Can you find the rule for giving another set of six numbers?

Polygonal numbers are those that are arranged in shapes as they enlarge. Explore the polygonal numbers drawn here.

Sweets are given out to party-goers in a particular way. Investigate the total number of sweets received by people sitting in different positions.

It starts quite simple but great opportunities for number discoveries and patterns!

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?

In how many different ways can you break up a stick of 7 interlocking cubes? Now try with a stick of 8 cubes and a stick of 6 cubes.

In this game for two players, the idea is to take it in turns to choose 1, 3, 5 or 7. The winner is the first to make the total 37.

This challenge is about finding the difference between numbers which have the same tens digit.

This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

Find the sum and difference between a pair of two-digit numbers. Now find the sum and difference between the sum and difference! What happens?

Got It game for an adult and child. How can you play so that you know you will always win?

How can you arrange these 10 matches in four piles so that when you move one match from three of the piles into the fourth, you end up with the same arrangement?

Strike it Out game for an adult and child. Can you stop your partner from being able to go?

Use your addition and subtraction skills, combined with some strategic thinking, to beat your partner at this game.

Are these statements relating to calculation and properties of shapes always true, sometimes true or never true?