In the setup, I wrote three principles for this game:
- The first person will choose their first choice. Start from there.
- Someone going 2nd will never get worse than their second choice. Likewise, 3rd will never get worse than their third choice.
- So, on average someone chosen, say, 3rd, will get their 3rd choice or better.
That lets you eliminate some answers. B, D, and E are out. At most one person will get their fourth choice: the rest will have a better choice available. Same with third. At least two people will get the chance to choose their 1st or 2nd choice.
C is impossible if you count. The second choices are X, Y and Z. But everyone has X or Y as a first choice, so someone will choose X or Y first. That only leaves two second choices left: one of X/Y and Z. So there aren’t enough for three people to get their second choice.
A is CORRECT. Here’s a scenario that show’s it’s possible. Note that I did not draw this on my page. This is just a way to represent the information to make it clearer for the explanation.
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