17 or 19? Puzzle problem: bridge crossing at night


Say you have four lads that want to cross the bridge at night and only a max of two can do this at once. There is a catch: the lamp needs to be always with the guys that are crossing the bridge and also, the faster one needs to cross the brider at the pace of the slower one.

We have four guys: A, B, C, D, and they can cross the bridge in four different time frames: 1 minute, 2 minutes, 5 minutes and 10 minutes respectively. What is the best combinations to crossing and coming back over the bridge that will yield the smallest total time? At first I calculated 19, then 17 minutes.

Do you know a better solution?

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