A logician invites 6 of his logician friends to help him celebrate his birthday. Each of the 6 guests is wearing a hat which is either red, yellow, or blue, and the logician host informs them all that there is at least 1 of each color. After they eat the cake, the host stands up and exclaims there is a special party prize for the first person who can deduce what color hat is on their head. The party guests all looked around the room at each other but no one claimed the prize immediately. Suddenly all 6 guests stood up and correctly identify what color hat was on their head.
What were the colors of their hats and how did they know?
There are four options
A B C D
1 Red 2 Red 3 Red 2 Red
2 Yellow 1 Yellow 2 Yellow 2 Yellow
3 Blue 3 Blue 1 Blue 2 Blue <o:p></o:p>
It is a waiting game:
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Options A, B and C (transpose the colours as appropriate given the hats available)
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If the person in the red hat looks at the room and counts 2 yellow and 3 blue and he knows that there is one of each colour then he knows he is wearing red.<o:p></o:p>
A both people in yellow hats will know that the red hat man was alone by the same deduction and can see 3 blue hats and 1 yellow hat and 1 red hat. After waiting an appropriate time with no-one speaking then there must be 2 yellow hats as neither person in a yellow hat can confidently say they are alone. They should get this at the same time.<o:p></o:p>
The three people in the blue hats will know there are three blue hats by the two previous deductions.<o:p></o:p>
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If there are 2 red hats, 2 blue hats, and 2 yellow hats then no-one can confidently speak so they will know simultaneously that there are an equal distribution.
Hoopy
Solution
