Brain Teasers
The Lead Actor
Hans Ernest Froopaloop, Jr. is in a play with four relatives: his sister, mother, son, and daughter. Each of the five has a different dressing room:
Room A: small, borders rooms B and E
Room B: large, borders rooms A, C, D, and E
Room C: large, borders rooms B and D
Room D: small, borders rooms B, C, and E
Room E: large, borders rooms A, B, and D
Here are some facts:
1. The rooms of the lead actor in the play and his or her sibling border the same number of rooms.
2. The lead's room and his or her parent's room are the same size.
3. HEF Jr's room and his daughter's room do not border each other.
4. Each room borders at least one man's room and at least one woman's room.
Who is the lead actor?
Room A: small, borders rooms B and E
Room B: large, borders rooms A, C, D, and E
Room C: large, borders rooms B and D
Room D: small, borders rooms B, C, and E
Room E: large, borders rooms A, B, and D
Here are some facts:
1. The rooms of the lead actor in the play and his or her sibling border the same number of rooms.
2. The lead's room and his or her parent's room are the same size.
3. HEF Jr's room and his daughter's room do not border each other.
4. Each room borders at least one man's room and at least one woman's room.
Who is the lead actor?
Answer
HEF Jr's sister is the lead actor.From fact 4, we know that rooms A and C each border one man's room and one woman's room. So one of rooms B and E is occupied by a man and the other by a woman, and one of rooms B and D is occupied by a man and the other by a woman. If room B is occupied by a man, rooms D and E are occupied both by women. Similarly, if room B is occupied by a woman, rooms D and E are both occupied by men. So the occupants of rooms D and E are of the same gender.
Since there were two pairs of siblings, each different-gendered, fact 1 tells us that either one of rooms A and C was occupied by a man and the other by a woman, or one of rooms D and E was occupied by a man and the other by a woman. From previous reasoning, we can determine that one of rooms A and C was occupied by a man and the other by a woman.
Since there were only two men, rooms D and E were both occupied by women. And since rooms A, C, D, and E were occupied by three women and one man, room B must be occupied by a man.
Fact 3 tells us that the occupant of room B cannot be HEF Jr, so it must be his son. Therefore, the siblings in rooms A and C must be HEF Jr. and his sister, and one of them must be the lead actor. From fact 3, we have these two scenarios:
1.
Room A: HEF Jr.
Room B: Son
Room C: Sister
Room D: Daughter
Room E: Mother
2.
Room A: Sister
Room B: Son
Room C: HEF Jr.
Room D: Mother
Room E: Daughter
In either scenario, the mother's and the sister's rooms are the same size. And from fact 2, the sister is the lead.
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Comments
Nice, thanks for posting
WimpyKid, I don't know where you find these, but I'm sure glad you are sharing them here! I know this one won't be everyone's cup of tea, but I had a great time solving it. It is so unique, I had no preconceived notion how to attack it, as you would a typical logic grid. You have to use pure logic and invent the solution. Another for my fave's list!
Snowdog, I recommend drawing a possible floor plan of the building housing the dressing rooms, then putting HEF Jr. and his relationships into the rooms so no clues are contradicted.
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