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.

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

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.

Label the joints and legs of these graph theory caterpillars so that the vertex sums are all equal.

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.

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

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?

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

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?

A Sudoku based on clues that give the differences between adjacent cells.

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

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.

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?

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?

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

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

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

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.

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

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.

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

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

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

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

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?

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?

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

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?

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

Investigate the different ways that fifteen schools could have given money in a charity fundraiser.

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.

15 = 7 + 8 and 10 = 1 + 2 + 3 + 4. Can you say which numbers can be expressed as the sum of two or more consecutive integers?

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?

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?

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?

Solve this Sudoku puzzle whose clues are in the form of sums of the numbers which should appear in diagonal opposite cells.

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

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?

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?

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.

Use the differences to find the solution to this Sudoku.