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?

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

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

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.

Imagine a stack of numbered cards with one on top. Discard the top, put the next card to the bottom and repeat continuously. Can you predict the last card?

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?

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?

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

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

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?

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?

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

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?

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?

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

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.

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

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

An introduction to the binomial coefficient, and exploration of some of the formulae it satisfies.

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?

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.

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

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

Mr Smith and Mr Jones are two maths teachers. By asking questions, the answers to which may be right or wrong, Mr Jones is able to find the number of the house Mr Smith lives in... Or not!

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.

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

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

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.

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

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

Special clue numbers related to the difference between numbers in two adjacent cells and values of the stars in the "constellation" make this a doubly interesting problem.

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.

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.

How many solutions can you find to this sum? Each of the different letters stands for a different number.

This task encourages you to investigate the number of edging pieces and panes in different sized windows.

An irregular tetrahedron is composed of four different triangles. Can such a tetrahedron be constructed where the side lengths are 4, 5, 6, 7, 8 and 9 units of length?

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

How have "Warmsnug" arrived at the prices shown on their windows? Which window has been given an incorrect price?

A particular technique for solving Sudoku puzzles, known as "naked pair", is explained in this easy-to-read article.

A 2 by 3 rectangle contains 8 squares and a 3 by 4 rectangle contains 20 squares. What size rectangle(s) contain(s) exactly 100 squares? Can you find them all?

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

This Sudoku requires you to do some working backwards before working forwards.