Four People, One Flashlight

The problem
4 people · 1 flashlight · cross in 17 min?12510STARTEND≤ 2 can cross at once · move at slower pace

Four people must cross a bridge at night.

  • The bridge holds at most 2 people at a time.
  • A single flashlight must travel with whoever is crossing.
  • Their crossing times are 1, 2, 5, 10 minutes. Two crossing together move at the slower person's pace.

Get everyone across in 17 minutes. Is it possible?

Tempting (but wrong)
"use the fastest as escort" → 19 min1 + 2 →2 min1 ←1 min1 + 5 →5 min1 ←1 min1 + 10 →10 mintotal: 2 + 1 + 5 + 1 + 10 = 19 ✗

"Use the fastest person as escort." Person 1 walks each slow person across, then runs back:

StepTime
1 + 2 cross2
1 returns1
1 + 5 cross5
1 returns1
1 + 10 cross10
Total19

Two minutes over. Many people stop here and decide 17 is impossible.