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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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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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What do the numbers shaded in blue on this hundred square have in common? What do you notice about the pink numbers? How about the shaded numbers in the other squares?

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If you are given the mean, median and mode of five positive whole numbers, can you find the numbers?

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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?

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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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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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?

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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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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How long does it take to brush your teeth? Can you find the matching length of time?

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

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

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

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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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How many different rectangles can you make using this set of rods?

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

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

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Is it possible to place 2 counters on the 3 by 3 grid so that there is an even number of counters in every row and every column? How about if you have 3 counters or 4 counters or....?

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This 100 square jigsaw is written in code. It starts with 1 and ends with 100. Can you build it up?

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

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Have a go at this well-known challenge. Can you swap the frogs and toads in as few slides and jumps as possible?

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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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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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In this game for two players, take it in turns to shade one petal, or two petals next to each other. Is it better to go first or second?

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Can you complete this calculation by filling in the missing numbers? In how many different ways can you do it?

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Look carefully at the numbers. What do you notice? Can you make another square using the numbers 1 to 16, that displays the same properties?

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What happens when you add three numbers together? Will your answer be odd or even? How do you know?