One of the five people below, a right-handed dog owner with a peanut allergy, is an alien. Who is it?
- Of the three right-handed people, exactly two are wearing black shirts and exactly one has blue eyes.
- Of the three people with a peanut allergy, exactly two have blue eyes and exactly one owns a dog.
- Of the three dog owners, exactly two are right-handed and exactly one is wearing a black shirt.
- Of the three blue-eyed people, exactly two own dogs and exactly one is wearing a black shirt.
- Of the three people wearing black shirts, exactly two are allergic to peanuts.
- 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!
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.
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.