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100 islanders logic puzzle

Posted By: Stein Kulseth
Date: Monday, 24 August 2009, at 9:45 a.m.

In Response To: 100 islanders logic puzzle (Gregg Cattanach)

But there IS new news each day. The fact that nobody committed suicide during the first 10 days is new data each day.

No, not exactly. Everybody knows that noone is going to commit suicide on the first day - or indeed the first 8 days, so only on the ninth day does the blueeyed gain info from the fact that the 9 expected suicides do not happen.

So on day 1-8 there really are no new information, but only new conclusions following from the new info given on day 0. It is a bit hard to see exactly what this piece of information is, even though it is fairly easy to do the proof by induction thing. But it appears in the cascade of what people think that the other people think.

Eg. consider the blueeyed persons (BEPs) A,B,C,D,E,F,G,H,I,J

  • A thinks there are 9 BEPs,
  • A thinks that B thinks there are 8 BEPS
  • A thinks B thinks C thinks there are 7 BEPS
  • ...
  • A ts B ts C ts D ts E ts F ts G ts H ts I ts J ts there are 0 BEPS

Of course this also applies to any permutation of A-J. The new info from the oracle is that the last assumption here is impossible. And the next day it will be impossible to believe that anyone believes that anyone ... etc ... believes that there are 1 BEP.

And everyone knows this will happen for at least 9 days - However the BEPs hope that it will stop on the 9th day with 9 suicides, whereas the GEPs hope for 10 suicides on the 10th day.

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