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.

We're excited about this new program for drawing beautiful mathematical designs. Can you work out how we made our first few pictures and, even better, share your most elegant solutions with us?

Use the differences to find the solution to 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.

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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

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

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

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?

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?

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?

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

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

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

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

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?

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.

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.

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. . . .

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

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 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.

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?

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.

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?

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

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

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.

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?

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

A Sudoku with clues given as sums of entries.

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

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.

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

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?

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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

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