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

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?

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

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

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

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

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.

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.

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.

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?

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

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

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.

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.

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?

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

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

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?

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?

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.

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 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?

Have a go at this game which has been inspired by the Big Internet Math-Off 2019. Can you gain more columns of lily pads than your opponent?

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

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?

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 Sudoku puzzles that together lead to a complete solution.

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

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.

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.

Use the differences to find the solution to this Sudoku.

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

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?

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.

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?

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.

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?

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.

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?

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

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?

A game for 2 people. Take turns placing a counter on the star. You win when you have completed a line of 3 in your colour.