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Bridge Crossing
CombinatorialMedium
15 min
25 pts
Description
4 people cross bridge at night with one flashlight. Varying speeds, minimize total time.
Game Rules
Four people need to cross a bridge at night. They have one flashlight. Person A takes 1 min, B takes 2 min, C takes 5 min, D takes 10 min. Maximum 2 people can cross at once. What is the minimum time?
Examples
A and B cross (2 min), A returns (1 min)
C and D cross (10 min), B returns (2 min)
A and B cross again (2 min)
Total: 17 minutes
Hints
Minimize return trips
Fastest people should do the returning
Solution (Click to reveal)
Optimal: A+B cross (2), A returns (1), C+D cross (10), B returns (2), A+B cross (2). Total = 17 minutes.