Behold the solution to Doctor E's Revenge #4. If you forgot the actual question, click here to see it again
There were 8 possible sets of answers that Molly could have given. We are looking for the set that would have narrowed Loonette's choice to two possibilities:
| Is it < 500? | Is it a perfect square? | Is it a perfect cube? | Possibilities |
| Yes | Yes | Yes | 1 |
| Yes | Yes | No | 18 |
| Yes | No | Yes | 4 |
| Yes | No | No | 467 |
| No | Yes | Yes | 1 |
| No | Yes | No | 8 |
| No | No | Yes | 2 |
| No | No | No | 490 |
The only set of answers that Molly could have given was No, No, Yes, because that is the only set that would narrow the choice to two possibilities, 512 and 1000. We know that Molly's first two answers were incorrect, so the correct answers to the questions were Yes, Yes, Yes. That means the answer has to be 64.
This genre of problem is called a Big Comfy Couch problem. Doctor E recommends them highly.
There is no justification for the Olson twins. Some very creative justifications were given (Peter B. and Kimberly K. frighten me), and credit was assigned, but they were all either fiction, sophistry, or rationalization. There are many things in this world that just are mysteries that will never make sense. The Olson twins, and their popularity, fit into that category.
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