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

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 2 minutes for the son to cross the bridge, 3 3 minutes for the daughter, 5 5 for mom and 10 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 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.


The answer is 21.

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2 solutions

Guillermo Wenrich
Nov 30, 2014

First the son and daughter cross taking 3 min, then the son crosses back taking 2 min, then the mom and dad cross taking 10 min, then the daughter crosses back taking 3 min, then the son and daughter cross back taking a final 3 min, 3+2+10+3+3=21

That is the only way I found to cross the bridge in 21 minutes, great job!

By the way, can you prove that 21 minutes is the minimum ?

Shenal Kotuwewatta - 6 years, 6 months ago
Saya Suka
Apr 27, 2021

Answer
= ceiling[3,2] + 3 + ceiling[10,5] + 2 + ceiling[3,2]
= 3 + 3 + 10 + 2 + 3
= 21 minutes


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