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

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.

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?

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?

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

A few extra challenges set by some young NRICH members.

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?

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.

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

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

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

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.

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

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

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

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

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.

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

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.

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

Use the differences to find the solution to this Sudoku.

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.

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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?

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

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?"

A Sudoku that uses transformations as supporting clues.

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.

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?

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

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?

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

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

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

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

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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?

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?

A Sudoku based on clues that give the differences between adjacent cells.

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.