Five hikers, one lantern, one narrow bridge
Asked at Optiver, Jump Trading
Five hikers reach a narrow rope bridge after dark. They share one lantern, and the bridge safely holds at most two people at a time. Whoever crosses must carry the lantern, so it has to be walked back each time, it cannot be thrown.
Their crossing times, alone, are 1, 3, 6, 8, and 12 minutes. When two cross together they move at the slower person's pace.
What is the least total time for all five to get across, and what schedule achieves it?