Brain Teasers
Trixie's Preference
Trixie is the most athletic girl in her grade. She is a star player on the baseball, soccer, and basketball teams. Four boys, Al, Ben, Carl, and Dan have a crush on her. Because Trixie is so passionate about sports, she wants her boyfriend to play the same three sports she does. Here are some facts:
1. No two of the four boys plays the same number of the sports baseball, soccer, and basketball.
2. Only one boy plays baseball but not soccer, and this boy is either Al or Dan.
3. Only one boy plays basketball but not baseball, and this boy is either Ben or Carl.
4. Either Al and Carl both play baseball, or neither plays baseball.
5. Either Ben and Dan both play soccer, or neither plays soccer.
Who should Trixie date?
1. No two of the four boys plays the same number of the sports baseball, soccer, and basketball.
2. Only one boy plays baseball but not soccer, and this boy is either Al or Dan.
3. Only one boy plays basketball but not baseball, and this boy is either Ben or Carl.
4. Either Al and Carl both play baseball, or neither plays baseball.
5. Either Ben and Dan both play soccer, or neither plays soccer.
Who should Trixie date?
Answer
Trixie should date Carl.Fact 1 can only work if one of the four boys plays only one sport, another plays two sports, a third plays all three sports, and the last plays no sports at all.
From facts 4 and 5, we have four scenarios:
1. Al and Carl both play baseball and Ben and Dan both play soccer. This cannot work because now none of the boys can play no sports at all.
2. Neither Al nor Carl plays baseball, and neither Ben nor Dan plays soccer. This cannot work because now none of the boys can play all three sports.
3. Neither Al nor Carl plays baseball, and Ben and Dan both play soccer. But now neither Al nor Dan plays baseball but not soccer. So, from fact 2, this cannot work.
4. Al and Carl both play baseball, and neither Ben nor Dan plays soccer. Since the other three scenarios cannot work, this must be the correct one.
Since Carl plays baseball, fact 3 tells us that Ben plays basketball but not baseball. Now that we know that Al and Carl both play baseball and Ben plays basketball, Dan must be the one who plays no sports at all.
Since Dan does not play baseball, fact 2 tells us that Al plays baseball but not soccer. Now that we know that none of Al, Ben, and Dan play soccer, Carl must be the one who plays all three sports, and therefore the one that Trixie should date.
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