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It is possible to identify a particular card out of a pack of 15 with the use of some mathematical reasoning. What is this reasoning and can it be applied to other numbers of cards?

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

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

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.

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. . . .

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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 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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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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The number of plants in Mr McGregor's magic potting shed increases overnight. He'd like to put the same number of plants in each of his gardens, planting one garden each day. How can he do it?

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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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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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A few extra challenges set by some young NRICH members.

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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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Can you recreate these designs? What are the basic units? What movement is required between each unit? Some elegant use of procedures will help - variables not essential.

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

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

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in how many ways can you place the numbers 1, 2, 3 … 9 in the nine regions of the Olympic Emblem (5 overlapping circles) so that the amount in each ring is the same?

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

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

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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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Move your counters through this snake of cards and see how far you can go. Are you surprised by where you end up?

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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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How many different symmetrical shapes can you make by shading triangles or squares?

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Time for a little mathemagic! Choose any five cards from a pack and show four of them to your partner. How can they work out the fifth?

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

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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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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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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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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?

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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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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?