Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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?

Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

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?

Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

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

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.

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.

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?

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

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.

A Latin square of order n is an array of n symbols in which each symbol occurs exactly once in each row and exactly once in each column.

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.

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.

The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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

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.

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

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

Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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

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

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

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

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

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. . . .

A function pyramid is a structure where each entry in the pyramid is determined by the two entries below it. Can you figure out how the pyramid is generated?

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?

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

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

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

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!

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.

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

This Sudoku problem consists of a pair of linked standard Suduko puzzles each with some starting digits

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

What is the smallest perfect square that ends with the four digits 9009?

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

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

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

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

The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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