The bridge crossing with two torches

Question

Four people must cross a rickety bridge at night. The bridge holds at most two people at a time, and anyone on it must carry a torch. They take 1, 2, 5 and 10 minutes respectively to cross, and a pair walks at the slower person's pace.

With a single torch, the well-known best plan takes 17 minutes, because the torch has to be carried back for each new pair.

Now suppose they have two torches. What is the fastest possible time, and what plan achieves it?

Accepted Answer

Twelve minutes. No return trips. With two torches, split the four people into two pairs and give each pair a torch. Each pair crosses once and never comes back, because the torch travels with them. The bridge holds only two, so the pairs cross one after the other, and the total time is the sum of the two pairs' crossing times. Choosing the pairs. A pair's time is its slower member's time. The three ways to pair four people: - (10 with 1) and (5 with 2): 10 + 5 = 15 minutes. - (10 with 2) and (5 with 1): 10 + 5 = 15 minutes. - (10 with 5) and (2 with 1): 10 + 2 = 12 minutes. The best plan send…

The bridge crossing with two torches

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