# Hat Colour Puzzle

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Four friends are sitting on a tree. Each one of them is wearing a hat. They don’t know which coloured hat are they wearing but they do know that two of them have green hats and two of them have orange hats.

Adam is sitting on the top branch and he can see the hats of Billy and Cyrus. Billy is sitting on a branch above Cyrus and he can see Cyrus hat. Duke is sitting at the base of the tree. Branches are covering him fully and no one can see his hat.

Now they are not allowed to look upwards. Who do you think will shout the colour of his hat first?

SherlockHolmes Expert Asked on 23rd April 2024 in

Yodha Expert Answered on 23rd April 2024.

If Billy and Cyrus are wearing same coloured hats, Adam sitting on the top branch can instantaneously decipher that he (and Duke) are wearing the other colour, and can announce it right away. In that case, all others can also decipher colours of their own hats once Adam makes the announcement.

If  Billy and Cyrus are wearing  hats of different colours, Adam can’t decipher the colour of his hat because it can be either colour AND he can’t see Duke’s hat. In that case, Billy, who can see Cyrus, can deduce that he is wearing the other colour hat (other than which colour Cyrus is wearing). Subsequently, Cyrus can also decipher his own colour.  Both Adam and Duke will remain unaware of their own colours.

Viji_Pinarayi Expert Answered on 23rd April 2024.

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