Spot the Alien: Blue Eyes and Black Shirts

One of the five people below, a right-handed dog owner with a peanut allergy, is an alien. Who is it?

Clues:

  1. Of the three right-handed people, exactly two are wearing black shirts and exactly one has blue eyes.
  2. Of the three people with a peanut allergy, exactly two have blue eyes and exactly one owns a dog.
  3. Of the three dog owners, exactly two are right-handed and exactly one is wearing a black shirt.
  4. Of the three blue-eyed people, exactly two own dogs and exactly one is wearing a black shirt.
  5. Of the three people wearing black shirts, exactly two are allergic to peanuts.

People:

  • Andy owns a dog and has brown eyes.
  • Beatrice has a peanut allergy and is not wearing a black shirt.
  • Carlos is right-handed and is wearing a black shirt.
  • Diane owns a dog and has blue eyes.
  • Edgar has a peanut allergy and is wearing a black shirt.

Who is the alien?

Scroll down for the answer!

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Answer:

We could solve this through the brute-force method of assuming each of the five people is an alien and eliminating them one by one, but let’s use a more elegant method.

In the chart below, we use R to denote right-handed people, S for people wearing black shirts, E for people with blue eyes, P for people with a peanut allergy, D for dog owners, and lower-case letters for people that don’t have these traits. We use A, B, C, D and E in the column headers to reference individuals who have particular combinations of traits.

ABCDE
1, 4REReRerErE
4, 3REDReDRedrEDrEd
3, 4REDsReDSRedSrEDsrEdS
2, 5REDsPReDSpRedSPrEDsprEdSP

From clues 1 and 4, we know that there are three right-handed people and three blue-eyed people, and only one person is both; therefore, one right-handed person has blue eyes (A), two do not (B and C), and the two people who are not right-handed both have blue eyes (D and E).

From clue 4, we know that one of the people without blue eyes (B and C, who both happen to be right-handed) must be a dog owner and one is not. From clue 3, we know two dog owners are right-handed, so the remaining right-handed person (A) must be a dog owner. Of the two people who are not right handed and have blue eyes (D and E), one must own a dog and one does not.

From clues 3 and 4, we know that the two people who do not own a dog and the two people who do not have blue eyes all wear black shirts. This would be the person who does not have blue eyes but owns a dog (B), the person who does not have blue eyes and does not own a dog (C) and the person who has blue eyes and does not own a dog (E). The remaining people (A and D) do not wear black shirts.

From clue 2, we know that the two people who do not own a dog (C and E) must both have a peanut allergy. Both of these people are wearing black shirts, so from clue 5 we know that the remaining person wearing a black shirt (B) does not have a peanut allergy. We know that there is a right-handed dog owner with a peanut allergy (the alien), so the remaining person who is right-handed and owns a dog (A) must have a peanut allergy, and be the alien. The last remaining person (D) does not have a peanut allergy.

Now we just need to identify which of the five people could be person A, the alien, who is right-handed, has blue eyes, has a dog, is not wearing a black shirt, and has a peanut allergy. The alien is in fact the only person who is not wearing a black shirt and has a peanut allergy; therefore, Beatrice, who matches these two characteristics, must be the alien.

The puzzlemonster. Lifelong puzzle maker, animal lover, total nerd. Husband to Android developer.

About Eric

The puzzlemonster. Lifelong puzzle maker, animal lover, total nerd. Husband to Android developer.

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