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.

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

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

Five numbers added together in pairs produce: 0, 2, 4, 4, 6, 8, 9, 11, 13, 15 What are the five numbers?

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?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

Each clue in this Sudoku is the product of the two numbers in adjacent cells.

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

A few extra challenges set by some young NRICH members.

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.

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

You need to find the values of the stars before you can apply normal Sudoku rules.

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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

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

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?

This Sudoku, based on differences. Using the one clue number can you find the solution?

Given the products of adjacent cells, can you complete this Sudoku?

Whenever a monkey has peaches, he always keeps a fraction of them each day, gives the rest away, and then eats one. How long could he make his peaches last for?

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.

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

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.

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

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

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.

A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

A Sudoku that uses transformations as supporting clues.

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

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

Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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

A Sudoku with clues given as sums of entries.

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

Four small numbers give the clue to the contents of the four surrounding cells.

A pair of Sudoku puzzles that together lead to a complete solution.

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

Can you use your powers of logic and deduction to work out the missing information in these sporty situations?

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?

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.

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

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.