Problem Statement of Bridge and Torch Puzzle

Four people need to cross a bridge at night, but there are specific rules and constraints:

1. Crossing Constraints:
   • Only two people can cross the bridge at the same time.
   • They have only one torch, and the bridge is too dangerous to cross without it.
   • The torch must be carried by someone when crossing, and it cannot be thrown across.
2. Individual Crossing Times:
   • Person A: Takes 1 minute to cross.
   • Person B: Takes 2 minutes to cross.
   • Person C: Takes 5 minutes to cross.
   • Person D: Takes 10 minutes to cross.
3. Movement Rule:
   • When two people cross together, they must move at the pace of the slower person. Basically, the higher time of two people crossing the bridge will be considered.

Objective: All four people must cross the bridge within 17 minutes or less.

Bridge and Torch Puzzle Solution

To solve this puzzle, follow these steps, keeping in mind the need to optimize the crossing times, especially for the slowest members:

1. Step 1: First Crossing (A and B together)
   • Who crosses? Person A (1 minute) and Person B (2 minutes).
   • Time taken: 2 minutes (Person B's speed).
   • Status: Person A and Person B have crossed the bridge, while Person C and Person D are still on the original side.
   • Time elapsed: 2 minutes.
2. Step 2: Return Trip (A returns with the torch)
   • Who returns? Person A (1 minute).
   • Time taken: 1 minute.
   • Status: Person A is back on the original side with the torch. Person B is waiting on the other side.
   • Time elapsed: 3 minutes.
3. Step 3: Second Crossing (C and D together)
   • Who crosses? Person C (5 minutes) and Person D (10 minutes).
   • Time taken: 10 minutes (Person D's speed).
   • Status: Person C and Person D have crossed the bridge, joining Person B on the other side.
   • Time elapsed: 13 minutes.
4. Step 4: Return Trip (B returns with the torch)
   • Who returns? Person B (2 minutes).
   • Time taken: 2 minutes.
   • Status: Person B is back on the original side with the torch. Person C and Person D are on the other side.
   • Time elapsed: 15 minutes.
5. Step 5: Final Crossing (A and B together)
   • Who crosses? Person A (1 minute) and Person B (2 minutes).
   • Time taken: 2 minutes (Person B's speed).
   • Status: Person A and Person B have crossed the bridge, joining Person C and Person D.
   • Time elapsed: 17 minutes.

Summary of the Solution

• Key Points:
  • The slowest members (Person C and Person D) only cross the bridge once.
  • The fastest member (Person A) crosses the bridge multiple times to minimize overall time.
  • The solution achieves the goal of getting everyone across in exactly 17 minutes.