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Four person crossing collapsing bridge & torch puzzle:
- Four persons wants to cross a bridge at night.
- There is one torch and persons can not cross the bridge without a torch.
- At max only two person can cross a bridge otherwise it will collapse.
- Each person takes different times to cross the bridge.
- 1 min, 2 mins, 7 mins and 10 mins.
- What is minimum time needed for all four persons to cross the bridge?
Solution of four person crossing bridge puzzle
- We need to address followings in current puzzle.
- How the slowest persons can cross the bridge?
- Slowest persons shall cross the bridge together.
- How best we can utilize the fastest persons?
- We will utilize fastest person to bring torch from destination to source end.
- For convenience, we will name the person as per their timings.
- Person crosses the bridge in 1 mins will be named as Person 1
- Person crosses the bridge in 7 mins will be named as Person 7
- Let us calculate the timing from S (source) end to D (destination) end using following options.
- Option 1 : (S [1, 2, 7, 10] and D[Nothing])
- Person 1 and Person 2 crosses the bridge. (S [7, 10] and D[1, 2])
- Person 2 comes back to S end (with torch). (S [2, 7, 10] and D[ 1])
- Total time = 2 + 2 = 4 mins
- Person 7 and Person 10 crosses the bridge. (S [2] and D[ 1, 7, 10])
- Total time = 4 + 10 = 14 mins
- Person 1 comes back to S end (with torch) (S [1, 2] and D[ 7, 10])
- Total time = 14 + 1 = 15 mins
- Person 1 and Person 2 crosses the bridge. (S [Nothing] and D[ 1, 2, 7, 10])
- Total time = 15 + 2 = 17 mins
- Four people crosses the bridge in 17 mins
- Option 2 : (S [1, 2, 7, 10] and D[Nothing])
- Person 1 and Person 2 crosses the bridge. (S [7, 10] and D[1, 2])
- Person 1 comes back to S end (with torch). (S [1, 7, 10] and D[ 2])
- Total time = 2 + 1 = 3 mins
- Person 7 and Person 10 crosses the bridge. (S [1] and D[ 2, 7, 10])
- Total time = 3 + 10 = 13 mins
- Person 2 comes back to S end (with torch) (S [1, 2] and D[ 7, 10])
- Total time = 13 + 2 = 15 mins
- Person 1 and Person 2 crosses the bridge. (S [Nothing] and D[ 1, 2, 7, 10])
- Total time = 15 + 2 = 17 mins
- Four people crosses the bridge in 17 mins
