In the dead of night, four people need to cross a rickety bridge. Unfortunately, they have only one torch and the bridge is too dangerous to cross without one.
The bridge is only strong enough to support two people at a time. Not all people take the same time to cross the bridge:
- 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.
When two people cross the bridge together, they must move at the slower person’s pace.
Can they all get across the bridge in less than 17 minutes, and if yes, how?
It is possible – here we go!
- Step 1: Person A, who can cross the bridge in 1 minute, and Person B, who can cross in 2 minutes, start their journey across the bridge together. Since they must move at a slower pace, their crossing takes 2 minutes in total.
- Step 2: Once they reach the other side, Person A, being the faster one, takes the torch and heads back to the starting side. This additional trip takes Person A 1 more minute, bringing the total elapsed time to 3 minutes.
- Step 3: On the starting side again, Person A passes the torch to Person C (5 minutes) and Person D (10 minutes). These two then cross the bridge together, moving at the pace of Person D. This takes 10 minutes, so the total time spent is now 13 minutes.
- Step 4: Upon reaching the other side, Person B now takes the torch and returns to the starting side to get Person A. Person B crosses the bridge in 2 minutes, bringing the total time to 15 minutes.
- Step 5: For the final crossing, Person A and Person B go together one last time, moving at Person B’s pace, thus taking 2 more minutes. This brings the total time spent to 17 minutes, meaning all four individuals have successfully crossed the bridge within the time limit.