Explaining, convincing and proving
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problemIs It Magic or Is It Maths?
Here are three 'tricks' to amaze your friends. But the really clever trick is explaining to them why these 'tricks' are maths not magic. Like all good magicians, you should practice by trying them. Can you explain how they work?
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problemKönigsberg
Can you cross each of the seven bridges that join the north and south of the river to the two islands, once and once only, without retracing your steps?
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problemClocked
Is it possible to rearrange the numbers 1,2......12 around a clock face in such a way that every two numbers in adjacent positions differ by any of 3, 4 or 5 hours?
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problemChildren at Large
There are four children in a family, two girls, Kate and Sally, and two boys, Tom and Ben. How old are the children?
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problemSeven Squares - Group-Worthy Task
Choose a couple of the sequences. Try to picture how to make the next, and the next, and the next... Can you describe your reasoning?
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problemTotal Totality
Is it possible to arrange the numbers 1-6 on the nodes of this diagram, so that all the sums between numbers on adjacent nodes are different?
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problemSo Many Sums
In this addition each letter stands for a different digit, with S standing for 3. What is the value of YxO?
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problemMagical Products
Can you place the nine cards onto a 3×3 grid such that every row, column and diagonal has a product of 1?