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

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.

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?

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

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?

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.

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.

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 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?

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

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?

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.

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.

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

A Sudoku that uses transformations as supporting clues.

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?

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?

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

Use the interactivity to listen to the bells ringing a pattern. Now it's your turn! Play one of the bells yourself. How do you know when it is your turn to ring?

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

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

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.

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

Arrange the digits 1, 1, 2, 2, 3 and 3 so that between the two 1's there is one digit, between the two 2's there are two digits, and between the two 3's there are three digits.

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

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 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?

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?

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?

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?

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

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

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.

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?

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?

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.

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

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

There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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.

If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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...

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