Prison Cell Problem
In Transum prison there are 100 prisoners in cells numbered 1 to 100.
On day 1, the guard turns the key in every lock to open every cell.
On day 2, the guard turns the key in every cell which is a multiple of 2. This locks all the even numbered cells.
On day 3, the guard turns the key in every cell which is a multiple of 3, locking or unlocking them.
On day 4, the guard turns the key in every cell which is a multiple of 4, locking or unlocking them.
This continues for one hundred days. The prisoners whose cells are open after the 100th day are set free. Which prisoners will be set free?
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| 25, 27, 28 etc |
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[Teacher's notes:- Click on the cell lock to unlock or lock a cell. Students should devise their own methods of working on this problem once the problem has been explained using this visual aid.
Discussions of solution methods may include the idea of multiples, factors and square numbers]
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