Solution
The Bridge at Night
Show the problem again
Four people must cross a bridge at night with one flashlight; at most two can cross at a time, and any crossing party moves at the slower member's pace. Their individual crossing times are 1, 2, 5, and 10 minutes, and the flashlight must be walked back (never thrown). What is the minimum total time, in minutes, for all four to cross?
Worked solution
The answer is 17 minutes. The trick is sending the two slowest together so their times overlap. Cross 1 & 2 (2 min), return 1 (1 min), cross 5 & 10 (10 min), return 2 (2 min), cross 1 & 2 (2 min): total 17. The greedy approach of always ferrying with the fastest person gives 19 and is a classic wrong answer.
Source: Classic river-crossing timing puzzle in wide circulation; no traceable original source. Statement written for AxiomIQ.