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

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

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.

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

Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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

Lorenzie was packing his bag for a school trip. He packed four shirts and three pairs of pants. "I will be able to have a different outfit each day", he said. How many days will Lorenzie be away?

How many models can you find which obey these rules?

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?

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.

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

Move from the START to the FINISH by moving across or down to the next square. Can you find a route to make these totals?

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?

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

A Sudoku with clues given as sums of entries.

Can you see who the gold medal winner is? What about the silver medal winner and the bronze medal winner?

How many different shapes can you make by putting four right- angled isosceles triangles together?

Let's suppose that you are going to have a magazine which has 16 pages of A5 size. Can you find some different ways to make these pages? Investigate the pattern for each if you number the pages.

El Crico the cricket has to cross a square patio to get home. He can jump the length of one tile, two tiles and three tiles. Can you find a path that would get El Crico home in three jumps?

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

In how many ways can you stack these rods, following the rules?

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?

Use the clues about the symmetrical properties of these letters to place them on the grid.

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

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?

Using the cards 2, 4, 6, 8, +, - and =, what number statements can you make?

How many different ways can you find of fitting five hexagons together? How will you know you have found all the ways?

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?

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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.

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

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?

In this maze of hexagons, you start in the centre at 0. The next hexagon must be a multiple of 2 and the next a multiple of 5. What are the possible paths you could take?

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

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

Frances and Rishi were given a bag of lollies. They shared them out evenly and had one left over. How many lollies could there have been in the bag?

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

Moira is late for school. What is the shortest route she can take from the school gates to the entrance?

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.

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?

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.

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

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

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?

What is the smallest number of tiles needed to tile this patio? Can you investigate patios of different sizes?

This train line has two tracks which cross at different points. Can you find all the routes that end at Cheston?

Vincent and Tara are making triangles with the class construction set. They have a pile of strips of different lengths. How many different triangles can they make?

The brown frog and green frog want to swap places without getting wet. They can hop onto a lily pad next to them, or hop over each other. How could they do it?