# Dwarfs on Island riddle

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On an Island, lives a population of highly intelligent dwarfs. The dwarfs all look exactly alike, but only differ in the fact that they are wearing either a red or a blue hat. Striking however, is that none of the dwarfs knows what the colour of his or her hat is. This is because it is forbidden to speak about the colour of the hats, and there no mirrors on the island. Nevertheless, the dwarfs do know that there is at least one dwarf with a red hat.

Once every century, there is a big party on the island, to which initially all dwarfs will go. However, this party is only intended for dwarfs wearing a blue hat. Dwarfs with a red hat are supposed not to return to the party the next day, as soon as they know that they are wearing a red hat.

How many days did it take before there were no more dwarfs with a red hat left at the last party, if you know that there were then 250 dwarfs with a red hat and 150 dwarfs with a blue hat?

SherlockHolmes Expert Asked on 20th November 2018 in

250 days.
In general:
suppose there are N dwarfs with a red hat
a dwarf with a red hat will see N-1 dwarfs with a  red hat
a dwarf with a blue hat will see N dwarfs with a red hat
If at day N there are still dwarfs with a red hat and you see only N-1 dwarfs with a red hat his means you have a red hat and should not return the next day.

CugelTheWise Expert Answered on 20th November 2018.

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