A group of ten students needed to travel home for the Holidays. Not more than three of them live in the same town. At least two of them would like to visit their fellow classmates. One of them has a family member abroad. It would take the student who lives the furthest 14 hours to get home by car while it would only take the nearest student only an hour by train.

What would be the most efficient way for all the students to travel home for the Holidays?

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    $\begingroup$ I'm not sure if this puzzle contains enough information to logically deduce, well, anything. First of all, are we talking about cost efficiency, fuel efficiency, fastest route, shortest route, or something else? What kind of solutions would be acceptable? $\endgroup$ – Bass Dec 19 '18 at 17:35
  • $\begingroup$ If they were all traveling together, we'd only need to worry about the most efficient route to bring everyone home in time for the holidays. $\endgroup$ – Kimberly Chang Dec 19 '18 at 18:22
  • $\begingroup$ You seem to misunderstand Bass, there are multiple types of efficiency you didn't specify which you wanted to be solved for and it also doesn't seem like you've provided all the necessary information to solve for them. $\endgroup$ – gabbo1092 Dec 19 '18 at 19:13
  • $\begingroup$ "What would be the most efficient way for all the students to travel home for the Holidays?" - That is easy to answer. Use Star Trek's teletransport! $\endgroup$ – Victor Stafusa Dec 19 '18 at 19:16
  • $\begingroup$ We also need to know something along the lines of where each student lives. If 3 live due east of the school, 3 due south, 3 dues west, and 4 due north, that changes the answer from if they all live due south. $\endgroup$ – eye_am_groot Dec 19 '18 at 19:31

Well, the only answer I can come up with is

The nearest student lives 1 hour away by train. At least 2 students want to visit their classmates instead of going to their own hometown. Trivially, 9 students are at least two!

So, let’s

Put all 10 students onto the train to visit the guy who lives 1 hour away. Then all students “reach their final destination” in exactly 1 hour, the minimum time.


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