River Crossing River Bridge Torch Medium — Set 62

Medium River Crossing Puzzle #62

Title

Medium River Crossing Puzzle #62

Scenario

Bridge & Torch

Narrative

Four people must cross a rickety bridge at night with one torch. The bridge holds at most 2 people. Each pair crosses at the speed of the slower person. Minimize total crossing time.

Entities

• {"id":"p1","name":"Person A (1 min)","icon":"\ud83c\udfc3"}
• {"id":"p2","name":"Person B (2 min)","icon":"\ud83d\udeb6"}
• {"id":"p5","name":"Person C (5 min)","icon":"\ud83e\uddcd"}
• {"id":"p8","name":"Person D (8 min)","icon":"\ud83d\udc22"}

BoatCapacity

2

Constraints

• The bridge holds at most 2 people at once.
• The torch must be carried across and brought back — you cannot throw it.
• When two people cross together, they move at the slower person's speed.
• Crossing speeds: A=1 min, B=2 min, C=5 min, D=8 min.

Question

Describe a valid sequence of crossings that gets everyone to the other side without violating any constraint. What is the minimum number of trips required?

Solution

• {"trip":1,"direction":"\u2192","carrying":["A (1)","B (2)"],"leftBank":"C,D","rightBank":"A,B","note":"A and B cross together. Time: 2 min."}
• {"trip":2,"direction":"\u2190","carrying":["A (1)"],"leftBank":"A,C,D","rightBank":"B","note":"A returns with torch. Time: 1 min."}
• {"trip":3,"direction":"\u2192","carrying":["C (5)","D (8)"],"leftBank":"A","rightBank":"B,C,D","note":"C and D cross. Time: 8 min."}
• {"trip":4,"direction":"\u2190","carrying":["B (2)"],"leftBank":"A,B","rightBank":"C,D","note":"B returns with torch. Time: 2 min."}
• {"trip":5,"direction":"\u2192","carrying":["A (1)","B (2)"],"leftBank":"","rightBank":"All","note":"A and B cross. Time: 2 min. Total: 15 min."}

MinimumTrips

5

Hint

The first 2 move(s) of the solution are shown below to help you start.

PartialSolutionHint

• {"trip":1,"direction":"\u2192","carrying":["A (1)","B (2)"],"leftBank":"C,D","rightBank":"A,B","note":"A and B cross together. Time: 2 min."}
• {"trip":2,"direction":"\u2190","carrying":["A (1)"],"leftBank":"A,C,D","rightBank":"B","note":"A returns with torch. Time: 1 min."}