Photo:
THE MIRROR
Shortly before the end of the hike comes the dreaded bridge: a maximum of two people can cross it at the same time, the old construction cannot take more.
Because it's dark, you always have to have a flashlight with you when crossing.
But the four hikers only have one, which they therefore have to carry back and forth.
The four people cross the bridge at different speeds:
Person 1 takes one minute.
Person 2 takes two minutes.
Person 3 takes five minutes.
Person 4 takes ten minutes.
When two people walk together, they walk at the pace of the slower person.
How long does it take for the quartet to get to the other side?
The shortest possible time is sought.
The four need
17 minutes
together .
The trick is to have the two slowest people (3 + 4) cross the bridge together.
In order for this to be possible, first people 1 and 2 go to the other side together.
That takes two minutes.
Next, person 1 goes back to people 3 and 4 alone with the lamp - this takes a minute.
Person 1 passes the lamp to the two.
3 and 4 then go to the opposite side in ten minutes, where they pass the lamp to person 2.
This finally fetches the person 1 waiting on the other side, which takes four minutes - two minutes there and two back.
Overall, crossing takes so
2+1+10+2+2 = 17 minutes.
A different order is also possible, which also lasts 17 minutes.
Instead of person 1, person 2 brings the lamp back to people 3 and 4 in step two. This then takes two minutes instead of one.
Persons 3 and 4 then go over the bridge together, as in the first solution.
At the end, person 1 picks up person 2 who is waiting on the other side, which only takes three minutes instead of four.
The total time is therefore also 17 minutes.
I found this puzzle on Steve Miller's Math Riddles website.
It is a variant of the bridge puzzle that was published here in 2015.
In case you missed a mystery from the past few weeks, here are the most recent episodes:
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