Re: Prisoner dilemma
I not quite sure if this is right but I think if one of the islanders, Maud, one day announces:
"Some of you have blue eyes"
then everyone apart from Maud dies.
If Dave and Maud were they only islanders with blue eyes then Dave would immediately know his eye colour and kill himself on day 1.
If Maud has blue eyes and two other guys, Mark and Dave, also have blue eyes. Mark and Dave would wait to see if the other killed themself on day 1 and then if they didnt they would both realise they had blue eyes and would die on day 2. Meanwhile Maud is none the wiser of her own eye colour. The same thing would have happened if she had brown eyes.
On day 3 everyone else would realise they had brown eyes and would die. Maud would still be clueless.
Im pretty sure the induction works in the same way as the previous example for three or more blue eyes non-Maud islanders.
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