Solution
An obvious first idea is that the cost of returning the torch to the people waiting to cross is an unavoidable expense which should be minimized. This strategy makes A the torch bearer, shuttling each person across the bridge:
| Elapsed Time | Starting Side | Action | Ending Side |
|---|---|---|---|
| 0 minutes | A B C D | ||
| 2 minutes | C D | A and B cross forward, taking 2 minutes | A B |
| 3 minutes | A C D | A returns, taking 1 minute | B |
| 8 minutes | D | A and C cross forward, taking 5 minutes | A B C |
| 9 minutes | A D | A returns, taking 1 minute | B C |
| 17 minutes | A and D cross forward, taking 8 minutes | A B C D |
This strategy does not permit a crossing in 15 minutes. To find the correct solution, one must realize that forcing the two slowest people to cross individually wastes time which can be saved if they both cross together:
| Elapsed Time | Starting Side | Action | Ending Side |
|---|---|---|---|
| 0 minutes | A B C D | ||
| 2 minutes | C D | A and B cross forward, taking 2 minutes | A B |
| 3 minutes | A C D | A returns, taking 1 minute | B |
| 11 minutes | A | C and D cross forward, taking 8 minutes | B C D |
| 13 minutes | A B | B returns, taking 2 minutes | C D |
| 15 minutes | A and B cross forward, taking 2 minutes | A B C D |
Read more about this topic: Bridge And Torch Problem
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