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Arrange the four number cards on the grid, according to the rules, to make a diagonal, vertical or horizontal line.

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

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

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Can you find all the ways to get 15 at the top of this triangle of numbers? Many opportunities to work in different ways.

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

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

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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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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 game you are challenged to gain more columns of lily pads than your opponent.

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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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10 space travellers are waiting to board their spaceships. There are two rows of seats in the waiting room. Using the rules, where are they all sitting? Can you find all the possible ways?

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How many ways can you find to do up all four buttons on my coat? How about if I had five buttons? Six ...?

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Can you arrange the digits 1, 1, 2, 2, 3 and 3 to make a Number Sandwich?

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

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

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

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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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Investigate the smallest number of moves it takes to turn these mats upside-down if you can only turn exactly three at a time.

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Hover your mouse over the counters to see which ones will be removed. Click to remove them. The winner is the last one to remove a counter. How you can make sure you win?

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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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Only one side of a two-slice toaster is working. What is the quickest way to toast both sides of three slices of bread?

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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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Can you work out the arrangement of the digits in the square so that the given products are correct? The numbers 1 - 9 may be used once and once only.

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Can you rearrange the biscuits on the plates so that the three biscuits on each plate are all different and there is no plate with two biscuits the same as two biscuits on another plate?

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How many possible necklaces can you find? And how do you know you've found them all?

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A few extra challenges set by some young NRICH members.

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Arrange 9 red cubes, 9 blue cubes and 9 yellow cubes into a large 3 by 3 cube. No row or column of cubes must contain two cubes of the same colour.

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This challenge is to design different step arrangements, which must go along a distance of 6 on the steps and must end up at 6 high.

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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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. . . .

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

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Mr McGregor has a magic potting shed. Overnight, the number of plants in it doubles. He'd like to put the same number of plants in each of three gardens, planting one garden each day. Can he do it?

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This task, written for the National Young Mathematicians' Award 2016, involves open-topped boxes made with interlocking cubes. Explore the number of units of paint that are needed to cover the boxes. . . .

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What is the largest 'ribbon square' you can make? And the smallest? How many different squares can you make altogether?

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The planet of Vuvv has seven moons. Can you work out how long it is between each super-eclipse?

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Take a rectangle of paper and fold it in half, and half again, to make four smaller rectangles. How many different ways can you fold it up?

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These activities focus on finding all possible solutions so working in a systematic way will ensure none are left out.

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This problem is based on a code using two different prime numbers less than 10. You'll need to multiply them together and shift the alphabet forwards by the result. Can you decipher the code?

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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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This challenge focuses on finding the sum and difference of pairs of two-digit numbers.

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This challenge, written for the Young Mathematicians' Award, invites you to explore 'centred squares'.

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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?