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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.

Read this article to find out more about the inspiration for NRICH's game, Phiddlywinks.

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

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

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

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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?

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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.

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

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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.

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

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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.

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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?

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

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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?

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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.

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

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

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.

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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?

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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?

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Four friends must cross a bridge. How can they all cross it in just 17 minutes?

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.

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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?

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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.

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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.

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

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

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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?

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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.

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

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

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It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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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?

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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?

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

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

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

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

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

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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?

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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?

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

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

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Gabriel multiplied together some numbers and then erased them. Can you figure out where each number was?

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