Four person crossing collapsing bridge & Torch puzzle

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])
    • Total time = 2 mins
  • 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])
    • Total time = 2 mins
  • 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