Funny five

Logic Level 3

Mr and Mrs Tan have five children - 4 boys and a girl. Their names are Alfred, Brenda, Charles, Darius and Eric.

For some reason, they refuse to tell each other their respective favourite colours.

However, they know each of them likes exactly one of the colours apricot, blue, cherry, dun and emerald such that none of them likes a colour that begins with the same letter as their name.

One day, the following weird discussion took place.

Brenda whispered into Alfred's ear, "I dislike apricot."

Alfred then whispered into Charles' ear, "And I really dislike cherry."

Eric, the youngest child, felt that this was pointless. He finally announced, "My favourite colour is dun."

Now Charles said to Alfred, "All these aren't helpful! I still cannot determine your favourite colour!"

Just then Alfred said to Brenda, "But sis, I do know your favourite colour now!"

Let's assume all five siblings are perfectly truthful and rational. What do you think Darius' favourite colour is?

Inconclusive Apricot Cherry Blue Emerald

1 solution

Noel Lo
Apr 3, 2016

From what Brenda said, Alfred knows her possible favourite colors are cherry and emerald. Dun is taken by Eric while blue and Brenda start with the same letter. Similarly, Charles knows Alfred's favourite color is either blue or emerald. Charles' favourite color is either apricot, blue or emerald.

For Charles to be unsure of Alfred's favourite color, his favourite color can't be blue or emerald otherwise he can take the other possible favourite color of Alfred. Hence he must like apricot. Since Alfred knows Brenda's favourite color, he must like a color common to his and Brenda's possible favourite colors which is emerald.

This means Brenda must like cherry which leaves blue for Darius.

I think you just took a little bit too fast of an approach , from what Brenda said Alfred will know that there are 2 colors of 5 that Brenda can't have (the color starting with her name and the other one she told Alfred) to which it needs to be added the color that Alfred has which is an information particularly known by Alfred and not by the readers therefore Brenda's favorite colors are in the way the readers can deduce one of those colors and not just 2 and while after it is made the announcement of Eric's favorite color the possible number of colors for Brenda will just get to 1 for Alfred and 2 for the readers.

Therefore it can be said that Alfred has one of the 3 possible colors of Brenda and that this same reasoning can't also be applied too for Charles who doesn't know after that announcement of Eric's favorite color which leads to your reasoning but it should be pointed out that from what Brenda said to Alfred the readers can just deduce that she can have 3 possible colors in contrast with Alfred who has one "covered" it may be said information even if this somehow tends to be more on a meta-logical side of reasoning based on what is possible to deduce and how but nice problem anyways.

A A - 5 years, 2 months ago

Funny five

1 solution

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