Bridge and torch problem facts for kids
The bridge and torch problem is a fun logic puzzle. It's about how four people can cross a narrow bridge at night. They only have one torch (flashlight) to light their way. This puzzle is part of a group called river crossing puzzles. These puzzles always involve moving things across a river with special rules.
The Story of the Bridge and Torch
Imagine four friends arriving at a river in the dark. There's a small bridge, but it's tricky! Only two people can cross it at the same time. They also have just one torch, and it's too dark to cross without it.
Each person crosses at a different speed:
- Person A is super fast, taking only 1 minute.
- Person B takes 2 minutes.
- Person C takes 5 minutes.
- Person D is the slowest, taking 8 minutes.
When two people cross together, they must walk at the speed of the slower person. For example, if A (1 minute) and C (5 minutes) cross, it will take them 5 minutes. The big question is: Can all four friends get across the bridge if the torch only lasts for 15 minutes?
Finding the Solution
At first, you might think the fastest person (A) should always carry the torch back and forth. Let's see what happens with that idea:
| 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 |
As you can see, this way takes 17 minutes. That's too long because the torch only lasts 15 minutes!
To solve the puzzle in time, you need a clever trick. The key is to make sure the two slowest people (C and D) cross together. This saves a lot of time! Here's how it works:
| 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 |
This strategy gets everyone across in exactly 15 minutes! It works because the two slowest people (C and D) cross together, so their slow time (8 minutes) only counts once for both of them. Then, one of the faster people (B) brings the torch back.
There's another way to do it that also takes 15 minutes. It's very similar, but the fast people (A and B) switch who brings the torch back in the middle steps. The main idea stays the same: the two fastest people cross first and last, and the two slowest people cross together in the middle.
See also
In Spanish: Acertijo del puente y la antorcha para niños
