The challenge
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?
Bridge and Torch Puzzle: 17-Minute Solution
Solve this hard optimization challenge, then compare your reasoning with the hint, checked answer, verification, and variation.
Hint
Compare the cost of using the fastest person as the only courier with using the two fastest together.
The 17-minute crossing plan
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.
Crossing ledger
- Send the 1-minute and 2-minute people across, then return the 1-minute person.
- Send the 7-minute and 10-minute people together, then return the 2-minute person.
- Send the 1-minute and 2-minute people across again for a total of 17 minutes.
Add the elapsed time
Add each crossing and return: 2 + 1 + 10 + 2 + 2 = 17. Everyone finishes on the far side and every crossing has the torch.
Compare strategies at the expensive step
Batch expensive work together. The locally fastest move is not always part of the globally fastest plan.
Why the fastest courier plan loses
Using the fastest person as the courier for every crossing feels efficient but makes the slow crossings happen separately and produces a longer total.
How confident were you?
Compare the two courier strategies
The expensive pair should cross together, but the torch must still return. Compare the cost of having the fastest person escort everyone with the cost of using the two fastest people as a shuttle team.
Recalculate after one crossing time changes
Replace the 10-minute person with a 12-minute person. Compare the two shuttle strategies again before choosing a schedule.
Study constraint satisfaction for problem solving for the reusable method behind this challenge. Then explore the logic puzzles and deductive reasoning learning path for connected examples and practice.