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

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By selecting digits for an addition grid, what targets can you make?

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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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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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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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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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Find the values of the nine letters in the sum: FOOT + BALL = GAME

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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?

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

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

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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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The letters in the following addition sum represent the digits 1 ... 9. If A=3 and D=2, what number is represented by "CAYLEY"?

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

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

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

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

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

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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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Play the divisibility game to create numbers in which the first two digits make a number divisible by 2, the first three digits make a number divisible by 3...

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Given the products of adjacent cells, can you complete this Sudoku?

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Different combinations of the weights available allow you to make different totals. Which totals can you make?

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

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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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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?

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

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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 differences to find the solution to this Sudoku.

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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?

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

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

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

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

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Each clue in this Sudoku is the product of the two numbers in adjacent cells.

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