Bridge Crossing Puzzle

An old classic that still trips people up in interviews. The obvious answer is not the best one.

Problem:

Four friends have to cross a rickety rope bridge at night with one torch; the bridge holds at most two people and cannot be crossed without the torch. They take 1, 2, 5 and 10 minutes to cross; a pair moves at the slower person's pace, and the torch must be carried back after each crossing. The obvious plan - let the 1-minute guy ferry everyone across - takes 19 minutes. Do better.

Solution:

Highlight the part between the * symbols for the answer.
* 17 minutes. Send the slow pair together: 1 and 2 cross (2), 1 returns (3), 5 and 10 cross (13), 2 returns (15), 1 and 2 cross (17). The two slow walkers must share a trip, else they alone burn 15 minutes, and a fast walker must wait on the far side to return the torch, so 1 and 2 cross first; the rest is forced. *

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