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.

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

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

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

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.

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.

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

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.

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

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?

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

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?

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.

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?

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

How many different symmetrical shapes can you make by shading triangles or squares?

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

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

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?

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?

A package contains a set of resources designed to develop students’ mathematical thinking. This package places a particular emphasis on “being systematic” and is designed to meet. . . .

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

This package contains a collection of problems from the NRICH website that could be suitable for students who have a good understanding of Factors and Multiples and who feel ready to take on some. . . .

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

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

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

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?

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?

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.

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

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.

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.

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

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

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

Different combinations of the weights available allow you to make different totals. Which totals can you make?

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

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

Use the differences to find the solution to this Sudoku.

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?

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

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.

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

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.

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

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?