Brain Teasers
Four Female Athletes
Four girls, Wanda, Xenia, Yolanda, and Zoe, are standing in a line. Exactly one girl plays baseball and soccer, but not basketball. Here are some facts:
1. Two girls who do not play baseball are standing next to Wanda.
2. Xenia is the only girl standing next to exactly one soccer player.
3. Yolanda is the only girl NOT standing next to exactly one basketball player.
Who plays baseball and soccer, but not basketball?
1. Two girls who do not play baseball are standing next to Wanda.
2. Xenia is the only girl standing next to exactly one soccer player.
3. Yolanda is the only girl NOT standing next to exactly one basketball player.
Who plays baseball and soccer, but not basketball?
Answer
Yolanda plays baseball and soccer, but not basketball.Fact 1 tells us that Wanda is standing between two girls. This means that she isn't on either end of the line. The two girls standing next to Wanda do not play baseball, so the girl who plays baseball and soccer but not basketball cannot be either of them. But maybe it could be Wanda.
If Wanda plays baseball and soccer but not basketball, fact 3 tells us that Yolanda is standing at the end of the line next to Wanda, since she is not standing next to any basketball players. But fact 2 contradicts this by telling us that Yolanda cannot be standing next to exactly one soccer player. So Wanda cannot play baseball and soccer but not basketball.
This leaves only the girl standing on the end NOT next to Wanda.
Now we must figure out where Yolanda is in THIS situation. If she's standing on the end next to Wanda, this means that Wanda does not play basketball, but then this would mean that the girl standing between Wanda and the girl on the end not next to Wanda is also standing between two non-basketball players. Similarly, Yolanda cannot be standing between Wanda and the girl who plays baseball and soccer but not basketball, which leaves us with our solution.
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Comments
Terrific logic puzzle. Another example of very few facts leading to a long series of deductions resulting in the solution. Pretty tough!
I think the solution could be more explicit, ending with "therefore Yolanda must be located at the end of the line, which we know is the girl who plays baseball and soccer, but not basketball." That could help some make the logic more clear. Then again, anyone who put enough effort into this puzzle to get to the last line of the solution may be logic fans anyway who could get if from the solution provided. This puzzle will scare off a lot of people.
I think the solution could be more explicit, ending with "therefore Yolanda must be located at the end of the line, which we know is the girl who plays baseball and soccer, but not basketball." That could help some make the logic more clear. Then again, anyone who put enough effort into this puzzle to get to the last line of the solution may be logic fans anyway who could get if from the solution provided. This puzzle will scare off a lot of people.
The scip model that I used to solve this one can be found at
https://gist.github.com/saska-gist/
1462d850f693b9760819d0ff518d68be
https://gist.github.com/saska-gist/
1462d850f693b9760819d0ff518d68be
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