What you see is not what you get #1 - The bridge problem

Discrete Mathematics Level 4

Once upon a time, a family with mom, dad, son and daughter was travelling in a dark night. They had only a single torch.

It takes \(2\) minutes for the son to cross the bridge, \(3\) minutes for the daughter, \(5\) for mom and \(10\) for dad.

Only two people can cross the bridge at the same time, else it will break. If two persons are going at the same time, the time it takes for them to cross the bridge is the time it takes for the slower one to cross the bridge.

(For example, if mom and dad are crossing the bridge at the same time, it will take \(10\) minutes)

Once the torch crosses the bridge, someone must bring it back if there are still people waiting to cross.

What is the minimum number of minutes it takes all four of them to cross the bridge?

Details and Assumptions:

  • They are humans and not wizards or fairies, so they cannot fly, and they don't have broomsticks or flying carpets or other fancy, magical stuff. Their torch is their only possession.
  • In this country, there are no jetpacks, hoverboards or similar things.
  • No one can throw the torch to the other side of the river.

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