riddle of the day

Crossing a bridge at night with just one flashlight seems like a speed problem. Maybe it's not entirely.

The bridge and the lantern

Reasoner
Timeless ingenuity

Riddle statement

Four people must cross a bridge at night. They only have one flashlight, and no one can cross without it. A maximum of two people can cross at a time. Each person takes a different time to cross:

  • 1 minute
  • 2 minutes
  • 5 minutes
  • 10 minutes

When two cross together, they take as long as the slowest one takes.

What is the shortest total time in which all four can cross?

Show solution

Solution

Answer: the shortest possible time is 17 minutes.

Let's call people by their times: 1, 2, 5 and 10.

The optimal strategy is:

  1. they cross 1 and 2: it takes 2 minutes;
  2. returns 1: takes 1 minute;
  3. they cross 5 and 10: it takes 10 minutes;
  4. returns 2: takes 2 minutes;
  5. 1 and 2 cross: it takes 2 minutes.

The total time is:

$ 2+1+10+2+2=17. $

The idea is to use the two fastest ones to carry the flashlight, but allow the two slowest ones to cross together only once. If the fastest one made all the returns, more time would be lost.