Favorite Color Puzzle

Logic Level 1

Two siblings, John and Amy, are discussing their favorite color. Their parents remember that one of their favorite colors is blue, and the other is red. If we know If at least one of them is lying, what is John's favorite color?

Blue Not enough information to determine Purple Red

2 solutions

Noel Lo
Aug 31, 2015

If one of them is lying, then that person must like the colour other than what he/she said. But this other colour would be the same colour suggested by the other person since there are only two colours. If this other person is telling the truth, then both people would like the same colour, resulting in a contradiction as the two people like different colours. Hence it cannot be that exactly one is lying while the other telling the truth- in other words both are lying. Since John's favourite colour is not red, it must be $\boxed{blue}$ .

I saw a problem like this "Bob and Andrew Problem", same logic.

Mark Cano - 5 years, 8 months ago

The problem grammar is unclear. The parents, grammatically, could have been talking about their own favorite colors, and the "lying" part could have applied to the parents as well.

I picked "not enough information" because I had thought this was a carefully worded trick question, but I was apparently wrong.

Sammy Berger - 4 years, 11 months ago

Omar Othman
Oct 10, 2015

This is a problem that can be systematically solved, without needing any brain power (sorry, I am a software engineer, so I have to know how to ask the brainless computer to solve my problem).

This is a simple truth table. Let $0$ means honest and $1$ means lying.

John = $0$ and Amy = $0$ <=> No way, we know one of them is lying.

John = $0$ and Amy = $1$ <=> This means both are red, no way. We know that both colors exist.

John = $1$ and Amy = $0$ <=> This means both are blue, no way. We know that both colors exist.

John = $1$ and Amy = $1$ <=> This means John is blue and Amy is red.

Job done.

Like this system of thinking but it is said that at least one of them is lying so both 0&0 is possible, right? Any case, That leads us that John favors blue (Y)

Amir latif - 5 years, 8 months ago

I think you reversed my notation. I wrote " $0$ means honest and $1$ means lying".

Maybe it doesn't make sense to you, but most computer programs return $0$ to the operating system if everything is fine, and a positive number (indicating the error code, which can be any of different problems, that's why they took the wider range of positive numbers) indicating failure. That's why I gave "honest" the number $0$ , because everything is fine if you are honest! :-D

Omar Othman - 5 years, 8 months ago

Wrong. Both need to lie. What if only one of them is lying? Correct answer is 3 not enough information.

Goran Došen - 4 years, 11 months ago

Favorite Color Puzzle

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