Solution to: Colourful DwarfsThe answer is: after 250 days there are no dwarfs with red hats left at the party.It is easiest to start from the situation where there is only 1 dwarf with a red hat. In that case, this dwarf would arrive at the party on the first day, and notice that he doesn't see any red hats. Since he knows that there should be at least 1 dwarf with a red hat, he concludes that he must have a red hat himself. As a consequence, the next day he doesn't show up at the party anymore. If there would be two dwarfs with red hats, they both would see 1 dwarf with a red hat on the first day. They know that if this dwarf doesn't return on the next day, he must have been the only one. If he returns, then there is no other conclusion then that they both must have a red hat. As a consequence, after 2 days they don't return to the party.
The situation where there are 250 red hats is identical,
only now it takes 250 days before all dwarfs with red hats can conclude that
they must have a red hat.
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