Brain Teasers
Three Men and Three Women in a Hotel
Three men, Ian, Jeff, and Kevin, and three women stayed in a hotel. Each of the six people stayed in a different one of these six rooms:
Room A: medium, borders rooms B and F
Room B: small, borders rooms A, C, and F
Room C: medium, borders rooms B, D, E, and F
Room D: small, borders rooms C and E
Room E: large, borders rooms C, D, and F
Room F: large, borders rooms A, B, C, and E
Ian said, "I stayed in a large room." Jeff said, "I stayed in a medium room." Kevin said, "I stayed in a small room." Exactly one of them lied.
Of the three rooms occupied by the men, only the liar's room bordered exactly two rooms occupied by women.
Who lied?
Room A: medium, borders rooms B and F
Room B: small, borders rooms A, C, and F
Room C: medium, borders rooms B, D, E, and F
Room D: small, borders rooms C and E
Room E: large, borders rooms C, D, and F
Room F: large, borders rooms A, B, C, and E
Ian said, "I stayed in a large room." Jeff said, "I stayed in a medium room." Kevin said, "I stayed in a small room." Exactly one of them lied.
Of the three rooms occupied by the men, only the liar's room bordered exactly two rooms occupied by women.
Who lied?
Answer
Ian lied.If the liar was in a large room, he didn't say, "I was in a large room." Ian, a truthteller, would have been in the other large room. A similar situation exists for the other rooms. Now we know that the room that was the same size as the liar's room was occupied by a truthteller.
If the liar bordered 4 rooms, 2 were occupied by women and 2 by men. The 1 remaining room must be occupied by a woman.
If the liar was in C, A was occupied by a man AND by a woman. If the liar was in F, D was occupied by a woman and E by a man. If C was occupied by a woman, the truthteller in E would have bordered 2 women, so C must have been occupied by a man. A and B must both have been occupied by women, but now the truthteller in C must border 2 women.
If the liar bordered 3 rooms, 2 were occupied by women and 1 by a man. 1 of the 2 remaining rooms was occupied by a man and 1 by a woman.
If the liar was in B, D was occupied by a man and E by a woman. C was occupied by a man, and A and F by women. But now the truthteller in C borders 2 women. If the liar was in E, F was occupied by a man and C and D by women. Exactly 1 of A and B was occupied by a woman, but this room plus C, both occupied by women, border F, occupied by a truthteller.
So the liar bordered 2 rooms, both occupied by women.
If the liar was in D, B was occupied by a man and C and E by women. But whether A or F was occupied by a woman, this room plus C, both occupied by women, would both have bordered B, occupied by a truthteller. So the liar was in A. This means that C was occupied by a man and B and F by women. If E was occupied by a man, it would have bordered 2 rooms occupied by women (D and F). So E was occupied by a woman and D by a man.
Now we know that C and D were both occupied by truthtellers. C must have been occupied by Jeff and D by Kevin, leaving only Ian.
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