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

A Sudoku with clues given as sums of entries.

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

Two sudokus in one. Challenge yourself to make the necessary connections.

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

Four numbers on an intersection that need to be placed in the surrounding cells. That is all you need to know to solve this sudoku.

Given the nets of 4 cubes with the faces coloured in 4 colours, build a tower so that on each vertical wall no colour is repeated, that is all 4 colours appear.

This pair of linked Sudokus matches letters with numbers and hides a seasonal greeting. Can you find it?

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

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

A Sudoku that uses transformations as supporting clues.

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

Two sudokus in one. Challenge yourself to make the necessary connections.

These are the faces of Will, Lil, Bill, Phil and Jill. Use the clues to work out which name goes with each face.

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

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

Given the products of diagonally opposite cells - can you complete this Sudoku?

Place the numbers 1 to 8 in the circles so that no consecutive numbers are joined by a line.

In this game for two players, you throw two dice and find the product. How many shapes can you draw on the grid which have that area or perimeter?

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.

Alice and Brian are snails who live on a wall and can only travel along the cracks. Alice wants to go to see Brian. How far is the shortest route along the cracks? Is there more than one way to go?

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?

This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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

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

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

A few extra challenges set by some young NRICH members.

Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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.

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.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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?

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

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

In this matching game, you have to decide how long different events take.

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?

Starting with four different triangles, imagine you have an unlimited number of each type. How many different tetrahedra can you make? Convince us you have found them all.

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

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?

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

In this Sudoku, there are three coloured "islands" in the 9x9 grid. Within each "island" EVERY group of nine cells that form a 3x3 square must contain the numbers 1 through 9.

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.

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