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Where Can We Visit?

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: x2 and -5. What do you think?

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Attractive Tablecloths

Charlie likes tablecloths that use as many colours as possible, but insists that his tablecloths have some symmetry. Can you work out how many colours he needs for different tablecloth designs?

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Egyptian Fractions

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18 Hole Light Golf

Age 5 to 16 Challenge Level:

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Try to switch off all the lights. Plan ahead and you will often beat the par score set by the computer.
 
Do you think all possible light patterns can be reached? Would you need to check all of them? Can you think of a small set of patterns which, if they were all reachable, would mean that all patterns were reachable?

Another version of this game is 9 Hole Light Golf, which can be found here.