Difficulty: Hard · Puzzle 5 of 6 · Topic: Classic Brain Teasers
Four people need to cross a bridge at night with one torch. At most two cross at once; pair speed is slower person's time. Times are 1, 2, 7, 10 minutes. Minimize total time.
Compare two strategies for moving the two slowest across.
1) Optimal pattern uses two fastest as shuttles.
2) Send 1 and 2 across: +2.
3) Send 1 back: +1 (total 3).
4) Send 7 and 10 across together: +10 (total 13).
5) Send 2 back: +2 (total 15).
6) Send 1 and 2 across: +2 (total 17).
7) Alternate strategy (1 with each slow person) costs 19, so 17 is minimum.Answer: Minimum total crossing time is 17 minutes.
Greedy 'always send fastest with slowest' gives 19 and misses global optimum.
For times 1, 2, 5, 10, what is the optimal total and why?