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.

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

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

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

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.

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

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.

Place the 16 different combinations of cup/saucer in this 4 by 4 arrangement so that no row or column contains more than one cup or saucer of the same colour.

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.

Use the differences to find the solution to this Sudoku.

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.

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

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

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

Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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

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?

A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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?

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

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.

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

A few extra challenges set by some young NRICH members.

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.

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.

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

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.

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

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.

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

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

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

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

If you take a three by three square on a 1-10 addition square and multiply the diagonally opposite numbers together, what is the difference between these products. Why?

An extra constraint means this Sudoku requires you to think in diagonals as well as horizontal and vertical lines and boxes of nine.

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.

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?

The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?