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Topic: Guards (Read 519 times) |
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R
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57 security guards are positioned so that no two pairs of guards are the same distance apart. Every guard watches the guard closest to him. Is there an arrangement of the guards so that every guard is being watched?
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towr
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Re: Guards
« Reply #1 on: Mar 19th, 2010, 2:41am » |
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If you have a series of guards where A watches B watched C etc, then each distance from one to the next is smaller, which means that last one cannot be watching A, because then A would also watch him.
So with the exception of isolated pairs of agents we have a graph without cycles). Which means the graph is a collection of pairs and trees, and in the trees the leaves are unwatched.
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Grimbal
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Re: Guards
« Reply #2 on: Mar 19th, 2010, 3:02am » |
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And with an odd number of guards, you can not have only 2-cycles (bi-cycles?).
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| « Last Edit: Mar 19th, 2010, 3:02am by Grimbal » |
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