You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

The challenge is to find the values of the variables if you are to solve this Sudoku.

Find all the ways of placing the numbers 1 to 9 on a W shape, with 3 numbers on each leg, so that each set of 3 numbers has the same total.

Advent Calendar 2011 - a mathematical activity for each day during the run-up to Christmas.

Try to solve this very difficult problem and then study our two suggested solutions. How would you use your knowledge to try to solve variants on the original problem?

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

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.

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?

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.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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

The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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?

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

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.

This is a variation of sudoku which contains a set of special clue-numbers. Each set of 4 small digits stands for the numbers in the four cells of the grid adjacent to this set.

You are given the Lowest Common Multiples of sets of digits. Find the digits and then solve the Sudoku.

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.

Each of the main diagonals of this sudoku must contain the numbers 1 to 9 and each rectangle width the numbers 1 to 4.

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.

I added together some of my neighbours house numbers. Can you explain the patterns I noticed?

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

Solve the equations to identify the clue numbers in this Sudoku problem.

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?

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

A pair of Sudokus with lots in common. In fact they are the same problem but rearranged. Can you find how they relate to solve them both?

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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.

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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

Take three whole numbers. The differences between them give you three new numbers. Find the differences between the new numbers and keep repeating this. What happens?

This Sudoku requires you to do some working backwards before working forwards.

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

Use the differences to find the solution to this Sudoku.

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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

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

Use the clues about the shaded areas to help solve this sudoku

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

A Sudoku that uses transformations as supporting clues.