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Is there an efficient way to work out how many factors a large number has?
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Take any four digit number. Move the first digit to the end and move the rest along. Now add your two numbers. Did you get a multiple of 11?
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Charlie and Abi put a counter on 42. They wondered if they could visit all the other numbers on their 1-100 board, moving the counter using just these two operations: ×2 and -5. What do you think?
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Liam's house has a staircase with 12 steps. He can go down the steps one at a time or two at time. In how many different ways can Liam go down the 12 steps?
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Can you maximise the area available to a grazing goat?
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Charlie and Alison have been drawing patterns on coordinate grids. Can you picture where the patterns lead?
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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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If you move the tiles around, can you make squares with different coloured edges?
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What is the greatest volume you can get for a rectangular (cuboid) parcel if the maximum combined length and girth are 2 metres?
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A tilted square is a square with no horizontal sides. Can you devise a general instruction for the construction of a square when you are given just one of its sides?
