POSSIBLE SOLUTIONS
A typical student's solution (name withheld).
Further Remarks
The solution above was not the best I have seen nor the worst, but it solved the problem and earned a high score. Many students get quite creative in their story line, and some are very careful to choose a route conducive to an interesting story. In more recent trials of this problem, I have told the students up front how much credit will be allotted to creativity which has noticeably improved the stories and made grading more enjoyable.
I have never had a group of students answer the Extra Credit problem, although being at an Engineering College, I feel inclined to keep offering.