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.

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

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.

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

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.

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?

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

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

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?

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

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

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?

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

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

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.

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

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.

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. . . .

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

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.

A Sudoku that uses transformations as supporting clues.

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

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

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.

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

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?

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

Given the products of diagonally opposite cells - can you complete this Sudoku?

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

A Sudoku with clues given as sums of entries.

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

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

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

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

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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?

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

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?