Four people need to cross a rickety bridge at night. Unfortunately, they have only one torch, and the bridge is too dangerous to cross without a torch. The bridge can support only two people at a time. Not all people take the same time to cross the bridge.
The crossing times for each person are:
- Person 1: 1 minute
- Person 2: 2 minutes
- Person 3: 7 minutes
- Person 4: 10 minutes
What is the shortest time needed for all four of them to cross the bridge?
Check if you were right - full answer with solution below.
Solution:
The initial solution most people will think of is to use the fastest person as an usher to guide everyone across. But it would take longer as 10 + 1 + 7 + 1 + 2 = 21 mins. But can it be the right answer? No.
To minimize the total time, the key idea is to have the two slowest people (7 and 10) cross together, so their combined slow time is counted only once. The fastest people (1 and 2) are used strategically for the return trips with the torch, keeping the time lost on return journeys as low as possible.
Steps:
Step 1: 1 and 2 cross the bridge together to the other side. Time taken: 2 mins. Running total: 2 mins.
Total time taken = 2 + 2 + 10 + 1 + 2 = 17 mins
Step 2: 2 returns with the torch from the other side. Time taken: 2 mins. Running total: 4 mins.
Step 3: 7 and 10 cross the bridge together to the other side. Time taken: 10 mins. Running total: 14 mins.
Step 4: 1 returns with the torch from the other side. Time taken: 1 min. Running total: 15 mins.
Step 5: 1 and 2 cross the bridge together to the other side. Time taken: 2 mins. Running total: 17 mins.
So , Minimum total time taken = 2 + 2 + 10 + 1 + 2 = 17 mins.