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Vandaag is het 18 February 2018

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Marching men - math puzzle

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A long and straight row of soldiers is marching with constant speed. The dog of the commander runs along the row from the end till the beginning, from the beginning till the end, from the end till the beginning etc. This takes always 2 minutes, 1 minute, 2 minutes, etc.
At some point the soldiers have to pass a very small bridge. However, the commander does not trust the strength bridge completely. He wonders how much time it will take them to pass the bridge when they stay marching with the same speed. How much time is that?

Explanation

It takes the dog 1 minute to run from the first to the last man. Then he runs 2 minutes from the last to the first man and then 1 minute back from the first man to the last man. So since the dog ran 2 minutes in both directions, after 4 minutes he is at the same point where he was 4 minutes ago. Since 4 minutes ago he was at the beginning of the row, and now he is at the end, this implies that it takes the marching soldiers 4 minutes to pass a point. So since the bridge was very small, they will also pass it in 4 minutes.