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

This sudoku requires you to have "double vision" - two Sudoku's for the price of one

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

This second Sudoku article discusses "Corresponding Sudokus" which are pairs of Sudokus with terms that can be matched using a substitution rule.

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

Pentagram Pylons - can you elegantly recreate them? Or, the European flag in LOGO - what poses the greater problem?

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.

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

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.

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

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?

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.

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.

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

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.

I added together some of my neighbours' house numbers. Can you explain the patterns I noticed?

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

What happens when you add three numbers together? Will your answer be odd or even? How do you know?

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

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

Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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

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

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

This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

Can you find a cuboid that has a surface area of exactly 100 square units. Is there more than one? Can you find them all?

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

Imagine you have an unlimited number of four types of triangle. How many different tetrahedra can you make?

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

Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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?

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.

Replace the letters with numbers to make the addition work out correctly. R E A D + T H I S = P A G E

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.

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

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?

Remember that you want someone following behind you to see where you went. Can yo work out how these patterns were created and recreate them?

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?

An investigation that gives you the opportunity to make and justify predictions.

This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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

Can you put the numbers 1-5 in the V shape so that both 'arms' have the same total?

This task, written for the National Young Mathematicians' Award 2016, focuses on 'open squares'. What would the next five open squares look like?

Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

Make your own double-sided magic square. But can you complete both sides once you've made the pieces?

Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

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