The bridge and the torch
Four people take 1, 2, 7, and 10 minutes to cross a narrow bridge. At most two can cross at once, they need one torch, and a pair moves at the slower person's pace. Can everyone cross in 17 minutes?
Optimization challenge at hard difficulty.
Hint
Compare the cost of using the fastest person as the only courier with using the two fastest together.
Answer and method
Yes. The 1 and 2 minute people cross (2). The 1 minute person returns (1). The 7 and 10 minute people cross (10). The 2 minute person returns (2). The 1 and 2 minute people cross again (2). Total: 17 minutes.
Reusable reasoning moveBatch expensive work together. The locally fastest move is not always part of the globally fastest plan.