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Cross the Bridge

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 is only strong enough to support two people at a time. Different persons take different times to cross the bridge. Times for each person to cross are: 1 min, 2 mins, 7 mins and 10 mins. What is the shortest time needed for all four of them to cross the bridge?

SOLUTION : Let us name the persons who take 1 min, 2 min, 7 min and 10 min as 1,2,7 and 10.

1 and 2 cross bridge, it takes 2 minutes. Then 2 comes back with the torch, it takes 2 minutes. Then 7 and 10 cross bridge, it takes 10 minutes. Then 1 comes back with the torch, it takes 1 minute. Then, 1 and 2 cross, it takes another 2 minutes.

So, Total time = 2 + 2 + 10 + 1 + 2 = 17 minutes

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