Given the products of adjacent cells, can you complete this Sudoku?

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?

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

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.

A mathematician goes into a supermarket and buys four items. Using a calculator she multiplies the cost instead of adding them. How can her answer be the same as the total at the till?

Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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.

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

A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

Ben passed a third of his counters to Jack, Jack passed a quarter of his counters to Emma and Emma passed a fifth of her counters to Ben. After this they all had the same number of counters.

Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

The clues for this Sudoku are the product of the numbers in adjacent squares.

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

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.

Find a cuboid (with edges of integer values) that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

Find the values of the nine letters in the sum: FOOT + BALL = GAME

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.

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?

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?

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

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?

Many numbers can be expressed as the sum of two or more consecutive integers. For example, 15=7+8 and 10=1+2+3+4. Can you say which numbers can be expressed in this way?

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

Can you arrange the numbers 1 to 17 in a row so that each adjacent pair adds up to a square number?

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

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

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?

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

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

A Sudoku that uses transformations as supporting clues.

My two digit number is special because adding the sum of its digits to the product of its digits gives me my original number. What could my number be?

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

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

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

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.

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.

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

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

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. . . .

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

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.

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