Brain Teasers
Mr. Froopaloop's Fiance
Hans Ernest Froopaloop, Jr. will marry one of three women: Audrey, Brenda, and Charlotte. Here are some facts:
1. Of Audrey and Brenda:
a. Either they both have blue eyes or neither has blue eyes.
b. One has red hair and the other does not.
2. Of Audrey and Charlotte:
a. Either they both have red hair or neither has red hair.
b. One is 5'11" and the other is not.
3. Of Brenda and Charlotte:
a. One has blue eyes and the other does not.
b. One is 5'11" and the other is not.
4. Of the three characteristics; blue eyes, red hair and 5'11":
a. If any of the three women has exactly two of the three characteristics, Mr. Froopaloop will marry the one with the least number of characteristics.
b. If any of the three women has exactly one of the three characteristics, Mr. Froopaloop will marry the one with the greatest number of characteristics.
Who will Mr. Froopaloop marry?
1. Of Audrey and Brenda:
a. Either they both have blue eyes or neither has blue eyes.
b. One has red hair and the other does not.
2. Of Audrey and Charlotte:
a. Either they both have red hair or neither has red hair.
b. One is 5'11" and the other is not.
3. Of Brenda and Charlotte:
a. One has blue eyes and the other does not.
b. One is 5'11" and the other is not.
4. Of the three characteristics; blue eyes, red hair and 5'11":
a. If any of the three women has exactly two of the three characteristics, Mr. Froopaloop will marry the one with the least number of characteristics.
b. If any of the three women has exactly one of the three characteristics, Mr. Froopaloop will marry the one with the greatest number of characteristics.
Who will Mr. Froopaloop marry?
Answer
Mr. Froopaloop will marry Charlotte.Facts 1a and 3a tell us that Charlotte is either the only one with blue eyes or the only one without blue eyes. Facts 1b and 2a tell us that Brenda is either the only one with red hair or the only one without red hair. Facts 2b and 3b tell us that Charlotte is either the only one who is 5'11" or the only one who isn't 5'11". Fact 4 tells us that no one woman can have one characteristic while another has two characteristics. This gives us two scenarios:
1. Audrey has blue eyes, does not have red hair, and is 5'11". Brenda has blue eyes, red hair, and is 5'11". Charlotte does not have blue eyes, does not have red hair, and is not 5'11".
2. Audrey does not have blue eyes, has red hair, and is not 5'11". Brenda does not have blue eyes, does not have red hair, and is not 5'11". Charlotte has blue eyes, red hair, and is 5'11".
Fact 4a tells us that in scenario 1, Mr. Froopaloop will marry Charlotte. Fact 4b tells us that in scenario 2, Mr. Froopaloop will marry...Charlotte.
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