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BGonline.org Forums
100 islanders logic puzzle - what about a silent oracle?
Posted By: Steve Mellen In Response To: 100 islanders logic puzzle - what about a silent oracle? (Gregg Cattanach)
Date: Friday, 21 August 2009, at 6:15 p.m.
Look at it this way. If there's only one blue-eyed islander, obviously the oracle's announcement is news to him, so he's going to kill himself on day 1 (we'll call the day of the oracle's announcement day 0). Nothing interesting there.
But what if there are two blue-eyed islanders? No one is actually getting new information, but each of the blue-eyed islanders thinks: "hey, there is only one blue-eyed islander, so this will be news to him! he'll kill himself tomorrow!" They'll both think that, and neither one will commit suicide. At which point they will both realize the only possible reason for that: I must have blue eyes too! And then both of them will commit suicide on day 2.
Now let's assume three blue-eyed islanders. All 3 of them think it's just like the prior example; hey, there are 2 guys with blue eyes, so they'll both end up killing themselves on day 2. And then when that doesn't happen, all 3 will realize: I must have blue eyes too! So the 3 of them end up committing suicide on day 3.
In general terms, excepting the trivial first scenario, everyone's thought process goes like this: "I can see X people with blue eyes. Either all X of them will commit suicide on day X, or else I must have blue eyes too."
So the oracle's announcement is not new information to anyone. The new information is finding out whether or not all the blue-eyed islanders you can see commit suicide on the expected day, or not. If they don't then you just found out you have blue eyes too.
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