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The computer has made a rectangle and will tell you the number of spots it uses in total. Can you find out where the rectangle is?

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Choose four different digits from 1-9 and put one in each box so that the resulting four two-digit numbers add to a total of 100.

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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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Join pentagons together edge to edge. Will they form a ring?

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Alison, Bernard and Charlie have been exploring sequences of odd and even numbers, which raise some intriguing questions...

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It's easy to work out the areas of most squares that we meet, but what if they were tilted?

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Charlie has made a Magic V. Can you use his example to make some more? And how about Magic Ls, Ns and Ws?

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Can you find a way to identify times tables after they have been shifted up or down?

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Play around with sets of five numbers and see what you can discover about different types of average...

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Here is a machine with four coloured lights. Can you develop a strategy to work out the rules controlling each light?

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Draw some quadrilaterals on a 9-point circle and work out the angles. Is there a theorem?

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Can you find out what is special about the dimensions of rectangles you can make with squares, sticks and units?

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Which armies can be arranged in hollow square fighting formations?

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Choose four consecutive whole numbers. Multiply the first and last numbers together. Multiply the middle pair together. What do you notice?

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Some students have been working out the number of strands needed for different sizes of cable. Can you make sense of their solutions?

Challenge Level

In this follow-up to the problem Odds and Evens, we invite you to analyse a probability situation in order to find the general solution for a fair game.