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?"

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.

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 adjacent cells, can you complete this Sudoku?

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

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?

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

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

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.

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?

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

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.

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

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

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

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?

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. . . .

A few extra challenges set by some young NRICH members.

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.

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

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

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?

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.

Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

Use the differences to find the solution to this Sudoku.

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.

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.

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

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?

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

Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: x2 and -5. What do you think?

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?

How many different symmetrical shapes can you make by shading triangles or squares?

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

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

Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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

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

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.

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

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?

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 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?