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Unformatted text preview: on the second day, everyone sends his two pieces of information two islands further on; on the third day, four islands further on; and on the fourth day, eight islands further on. For example, the pirate on island 8 would send his various pieces of information to islands 9, then 10, then 1, and finally 5. Why does this work? Since the scheme is the same for all the participants, we only need to see that the first piece of information is universally distributed. Look at island i , and write i1 as a sum of powers of 2. The powers appearing will tell you how the message got from island 1. For example, if i = 6, write 5 = 4 + 1; the message from 1 arrived at island 6 by going first to island 2 via a single island flight, followed by a four island flight. Exactly the same procedure solves the problem for 12 mutineeers. this page....
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 Spring '10
 AlbertoDelgado
 Combinatorics, Addition, Chess piece, Mike Fitzpatrick

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