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Given a set of points (x,y) with distinct x values, find a polynomial that goes through all of them, then prove some results about the existence and uniqueness of these polynomials.

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

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Show there are exactly 12 magic labellings of the Magic W using the numbers 1 to 9. Prove that for every labelling with a magic total T there is a corresponding labelling with a magic total 30-T.

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

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How many solutions can you find to this sum? Each of the different letters stands for a different number.

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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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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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Find the positive integer solutions of the equation (1+1/a)(1+1/b)(1+1/c) = 2

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

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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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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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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!

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.

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

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

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The clues for this Sudoku are the product of the numbers in adjacent squares.

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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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Ben, Jack and Emma passed counters to each other and ended with the same number of counters. How many did they start with?

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

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The puzzle can be solved by finding the values of the unknown digits (all indicated by asterisks) in the squares of the $9\times9$ grid.

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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.

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

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The items in the shopping basket add and multiply to give the same amount. What could their prices be?

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

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

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

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This Sudoku requires you to do some working backwards before working forwards.

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

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Here is a Sudoku with a difference! Use information about lowest common multiples to help you solve it.

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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?

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

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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?

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

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