Green for correct, yellow for neutral, red for wrong

Logic Level 2

Three siblings - Alfred, Brenda and Charles - like one of the colours green, yellow and red (not necessarily in the same order). When asked about their favourite colours, they gave the following answers:

  • Alfred - "Charles likes yellow."

  • Brenda - "Alfred likes red."

  • Charles - "Brenda likes green."

In their family, it is known that the green lover always tells the truth, the yellow lover sometimes tells the truth and sometimes lies while the red lover always lies. What is Brenda's favourite colour?

Green Red Yellow Not enough information to determine

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2 solutions

Noel Lo
Aug 31, 2015

First we zero in on who likes green. If Charles likes green, then there would be a contradiction as the statement that Brenda likes green would also be true which means two siblings like the same colour but we know all three favourite colours are different.

If Brenda likes green, then it would definitely be true to say that Alfred likes red as the green lover always tells the truth. It would follow that Charles likes yellow as that is the only colour left. But we have a contradiction. If Alfred likes red, then the statement that Charles likes yellow is definitely false as the red lover always lies.

Hence the only possible person who likes green is Alfred. It is therefore true to say that Charles likes yellow, leaving only one possible favourite colour for Brenda which is r e d \boxed{red} .

Saya Suka
Feb 16, 2021

One of the speakers is a truth teller, thus one of the colours is truly the favourite one of the people mentioned. On the other hand, by the same argument, we also have at least a liar among the 3, thus at least one person doesn't get matched with their favourite colour, but to really get a mismatch, you need 2 mistaken pairs, at the very least. Anyway, we now know that the green lover is the only one who told the truth, and whoever mentioned about the green lover must be lying. By this, Charles must be lying and Brenda does NOT like green as he claimed. Then, the only possibility left is that Alfred is the one who likes green and told the truth about Charles liking yellow, leaving Brenda's favourite colour to be RED.

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