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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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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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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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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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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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There are nine teddies in Teddy Town - three red, three blue and three yellow. There are also nine houses, three of each colour. Can you put them on the map of Teddy Town according to the rules?

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

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

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

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

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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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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A few extra challenges set by some young NRICH members.

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

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A monkey with peaches, keeps a fraction of them each day, gives the rest away, and then eats one. How long can his peaches last?

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

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

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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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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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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.

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

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

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

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Can you find six numbers to go in the Daisy from which you can make all the numbers from 1 to a number bigger than 25?

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

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

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

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

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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?

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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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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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A student in a maths class was trying to get some information from her teacher. She was given some clues and then the teacher ended by saying, "Well, how old are they?"

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Find the smallest whole number which, when mutiplied by 7, gives a product consisting entirely of ones.

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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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Just four procedures were used to produce a design. How was it done? Can you be systematic and elegant so that someone can follow your logic?