The challenge is to find the values of the variables if you are to solve this Sudoku.

Solve the equations to identify the clue numbers in this Sudoku problem.

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.

You have twelve weights, one of which is different from the rest. Using just 3 weighings, can you identify which weight is the odd one out, and whether it is heavier or lighter than the rest?

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?

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

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

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.

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

Problem solving is at the heart of the NRICH site. All the problems give learners opportunities to learn, develop or use mathematical concepts and skills. Read here for more information.

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.

This article for teachers describes several games, found on the site, all of which have a related structure that can be used to develop the skills of strategic planning.

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

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?

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

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

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...

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

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

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

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

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

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 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.

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

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

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

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

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

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.

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?

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?

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.

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?

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

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?

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?

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

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.

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?

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