Bridge Crossing Puzzle (1, 2, 5, 10) - The 17-Minute Solution

The setup

Four people cross a two-person bridge at night with one torch, at speeds of 1, 2, 5 and 10 minutes; a pair moves at the slower walker's pace. The storm hits in 17 minutes. How does everyone cross?

Short answer: 17 minutes exactly - by pairing the 5 and the 10 together so their crossings overlap: 1+2 across, 1 back, 5+10 across, 2 back, 1+2 across.

The schedule

Dee (1) and Cass (2) cross: 2 minutes. Dee walks the torch back: 1. Bo (5) and Amal (10) cross together: 10. Cass returns the torch: 2. Dee and Cass cross again: 2. Total 2 + 1 + 10 + 2 + 2 = 17.

Why the obvious strategy loses

The instinct is to use the fastest walker as a ferry: 1 escorts everyone, one at a time. That costs 10 + 1 + 5 + 1 + 2 = 19 minutes, because the two slow crossings (10 and 5) are both paid in full.

The winning idea is to make the two slowest cross TOGETHER, so the 5 is absorbed inside the 10 rather than added to it. The price is an extra return trip by a fast walker, +3 in total - a bargain against the 5 it saves. The general rule for such puzzles: when the two slowest are much slower than the two fastest, ship the slow pair together between fast-pair shuttle moves.

Why interviews ask it

Interviewers use this to watch for the moment you question the greedy assumption. The candidate who computes the ferry answer, notices 19 > 17, and goes hunting for overlapped cost is showing exactly the optimisation instinct the job wants.