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.

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

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

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?

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

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

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.

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 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.

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.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

A Sudoku that uses transformations as supporting clues.

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. . . .

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?

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?

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?

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

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?

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.

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.

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

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.

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.

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?

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

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?

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?

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

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?

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

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

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

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?

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

Explore this how this program produces the sequences it does. What are you controlling when you change the values of the variables?

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.

You need to find the values of the stars before you can apply normal Sudoku rules.

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

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?

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?

A Sudoku with clues given as sums of entries.