Can you put the 25 coloured tiles into the 5 x 5 square so that no column, no row and no diagonal line have tiles of the same colour in them?

Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?

You have been given nine weights, one of which is slightly heavier than the rest. Can you work out which weight is heavier in just two weighings of the balance?

in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

The NRICH team are always looking for new ways to engage teachers and pupils in problem solving. Here we explain the thinking behind maths trails.

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.

Bellringers have a special way to write down the patterns they ring. Learn about these patterns and draw some of your own.

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

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.

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.

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

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 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. . . .

If you have only 40 metres of fencing available, what is the maximum area of land you can fence off?

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

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.

Do you notice anything about the solutions when you add and/or subtract consecutive negative numbers?

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.

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

Use the interactivity to play two of the bells in a pattern. How do you know when it is your turn to ring, and how do you know which bell to ring?

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...

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".

A Sudoku with clues given as sums of entries.

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

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

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.

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?

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

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

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.

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

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

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.

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?

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

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?

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?

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?

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

This challenge extends the Plants investigation so now four or more children are involved.

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.

A challenging activity focusing on finding all possible ways of stacking rods.

This tricky challenge asks you to find ways of going across rectangles, going through exactly ten squares.

This challenging activity involves finding different ways to distribute fifteen items among four sets, when the sets must include three, four, five and six items.