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?

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?

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.

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.

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?

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

It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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

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

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?

This is about a fiendishly difficult jigsaw and how to solve it using a computer program.

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.

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.

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

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

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

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

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?

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.

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. . . .

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?

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.

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.

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.

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

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

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

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?

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

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

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

In this article, the NRICH team describe the process of selecting solutions for publication on the site.

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

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

Use the differences to find the solution to this Sudoku.

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

Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?

Can you swap the black knights with the white knights in the minimum number of moves?

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.