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?"

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...

Given the products of adjacent cells, can you complete 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.

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.

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.

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

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?

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?

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

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

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

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.

The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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?

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?

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

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

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.

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?

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

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

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

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?

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.

Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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

Use the differences to find the solution to this Sudoku.

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

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

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

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

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.

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

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?

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

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

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

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

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

This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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

First Connect Three game for an adult and child. Use the dice numbers and either addition or subtraction to get three numbers in a straight line.

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

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

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.