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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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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 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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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 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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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?

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

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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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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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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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A few extra challenges set by some young NRICH members.

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

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

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

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Design an arrangement of display boards in the school hall which fits the requirements of different people.

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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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These activities lend themselves to systematic working in the sense that it helps to have an ordered approach.

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

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An investigation involving adding and subtracting sets of consecutive numbers. Lots to find out, lots to explore.

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

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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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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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Draw some isosceles triangles with an area of $9$cm$^2$ and a vertex at (20,20). If all the vertices must have whole number coordinates, how many is it possible to draw?

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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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This task follows on from Build it Up and takes the ideas into three dimensions!

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Can you work out how many cubes were used to make this open box? What size of open box could you make if you had 112 cubes?

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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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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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These activities lend themselves to systematic working in the sense that it helps if you have an ordered approach.

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Can you put the numbers 1 to 8 into the circles so that the four calculations are correct?

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