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

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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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Many natural systems appear to be in equilibrium until suddenly a critical point is reached, setting up a mudslide or an avalanche or an earthquake. In this project, students will use a simple. . . .

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The letters of the word ABACUS have been arranged in the shape of a triangle. How many different ways can you find to read the word ABACUS from this triangular pattern?

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

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A few extra challenges set by some young NRICH members.

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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.

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

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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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Two sudokus in one. Challenge yourself to make the necessary connections.

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

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

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

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.

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Two sudokus in one. Challenge yourself to make the necessary connections.

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This Sudoku puzzle can be solved with the help of small clue-numbers on the border lines between pairs of neighbouring squares of the grid.

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The puzzle can be solved with the help of small clue-numbers which are either placed on the border lines between selected pairs of neighbouring squares of the grid or placed after slash marks on. . . .

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Rather than using the numbers 1-9, this sudoku uses the nine different letters used to make the words "Advent Calendar".

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

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

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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!

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

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Use the differences to find the solution to this Sudoku.

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60 pieces and a challenge. What can you make and how many of the pieces can you use creating skeleton polyhedra?

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

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

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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.

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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?

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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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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?

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

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

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A man has 5 coins in his pocket. Given the clues, can you work out what the coins are?

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

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

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A challenging activity focusing on finding all possible ways of stacking rods.

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

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A cinema has 100 seats. Show how it is possible to sell exactly 100 tickets and take exactly £100 if the prices are £10 for adults, 50p for pensioners and 10p for children.

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This cube has ink on each face which leaves marks on paper as it is rolled. Can you work out what is on each face and the route it has taken?

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Countries from across the world competed in a sports tournament. Can you devise an efficient strategy to work out the order in which they finished?