Forgetful parents
During a family party, Mr and Mrs Tan distributed four party hats to their four children. The hats came in four different colours, each of which is liked by one of their four children. Charles was supposed to wear the yellow hat, Darius the blue one, Brenda the red one and Alfred the green hat.
Unfortunately, Mr Tan made a blunder in distributing the party hats. Mrs Tan scolded him, saying that none of the four kids have a party hat of their favourite colour.
Each of the four kids could only see their own hat. Just then, Charles told Darius, "My hat is not X." X is a colour which is neither yellow nor the colour of the hat Darius received. Only Charles and Darius knew what X is. This alone was enough for the two older brothers to figure out what colour hats the four kids were given.
What was the colour of the hat Charles received?
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1 solution
Let's determine what X is. If Charles said his hat was not blue, then the blue hat could be either with Brenda or Alfred since neither like blue. But if Charles said his hat was not red, then he can pinpoint who received the red hat. If Darius' hat isn't red, then the only possible person with the red hat is Alfred since Brenda likes red. Similarly, if Charles said his hat isn't green, then the green hat must be with Brenda if Darius' hat isn't green. This means X is either red or green.
Now if Charles has a green or red hat if X is red/green respectively, then the one with a blue hat can be Brenda or Alfred as neither like blue. But if Charles has a blue hat, then by saying his hat isn't red, then the red hat wearer must be Alfred if Darius' hat isn't red. As Darius knows his hat colour, Brenda's hat colour must be the only colour left. Similarly, if Charles says his hat isn't green, then Brenda must be the wearer of the green hat. The rest follows similarly.