Puzzles and Problems

Some challenges to solve

The suspended bridge

An unfortunate family is followed by a pack of wolves in the rockies and the only way back to safety is through a suspended bridge. The suspended bridge holds no more than two persons. Additionally, it is dark and there is only one headlamp available, and one of several person can only cross with the headlamp as the bridge is patched with holes.

Each member of the family can cross in the following time:

  • mother 1 min
  • father 2 mins
  • son 5 mins
  • grand-mother 10 mins

Taking into account all back and forth, what is the minimum amount of time it takes for the whole family to reach the other side of the bridge ?

Solution

17 mins.

There are two keys to this optimization problem:

  • the fastest people need to be carrying the lamp back and forth
  • the slowest people need to travel together.

Following this, the mother and father go first (2 mins) then the father brings the lamp back (+2 mins = 4). Then the son and the grand-mother go together (+10 mins = 14). The mother brings the lamp back (+1 min = 15). And then the mother and the father cross (+2 mins = 17 mins).

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