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My college has a puzzle every week that students can try to answer and win $10. It's a social science college, so I don't know if they assume we're dumb and can't do logic or if this is really supposed to be a puzzle.

If a man walks due south for 4km, and then due north for 3km, what is the maximum distance he can be from the point where he started?

The obvious answer would be 1km, but that's not really a puzzle, is it? Unless they think we're that dumb. So I was trying to think of other answers. What throws me off is that a few of my friends were talking to the secretary about it, explaining that

someone could be near the South Pole, walking south, once he reaches the South Pole and continues, he would be going North, so the answer could be 7km.

But she implicitly said it was not it? So... What answers can you folks come up with?

Edit: Thanks folks, I guess the answer mentioned has to be the right one, even if they hadn't thought of it, they have to accept it

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  • $\begingroup$ How is distance around a sphere measured/defined in this case? A direct straight line from one point to the other (going through sphere), or the distance around the surface? $\endgroup$
    – GendoIkari
    Feb 15, 2018 at 16:12
  • $\begingroup$ Probably surface, but it doesn't say anything in the question, so I'm guessing that if you explain your reasoning, it should be fine $\endgroup$
    – fay
    Feb 15, 2018 at 16:16
  • $\begingroup$ if 7km is not the maximum distance, then it should be more than 7 (the south pole answer is valid, and should be accepted, even if they wait 1 km). $\endgroup$
    – dna
    Feb 15, 2018 at 16:24
  • $\begingroup$ Is the answer "1Km," and we are supposed to prove it or what? $\endgroup$
    – ibrahim mahrir
    Feb 15, 2018 at 16:40
  • 2
    $\begingroup$ The bear is white. $\endgroup$
    – user41531
    Feb 15, 2018 at 17:00

6 Answers 6

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Using the second most obvious answer:

He started 4km north of the South Pole, traveled south 4km, then kept walking in the same direction (which is now north) for 3km.

Ignoring the mostly-insignificant curve of the earth, that's

7km from his starting position.

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  • $\begingroup$ W.R.T. your remark about ignoring the curve of the Earth, yes, that's what we always do. We never take the curve of the Earth in account! If I travel to the other side of the world, I'm 20,000 km from home, not 12,732 km. $\endgroup$
    – Mr Lister
    Feb 18, 2018 at 18:13
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It could be that it's a lateral-thinking puzzle, in which case, I can think of two different outside-the-box answers.

Answer 1:

The man walks south for 4km and, as he finishes that walk, he boards a boat. The boat sails him to the other side of the world, at which point he walks north 3km, exiting the boat in the process. He is now exactly halfway around the world from where he started.

Answer 2:

On a universal scale, he is millions of miles away from where he was when he started, due to the movement of the Earth around the sun, the movement of the sun around the Milky Way, the movement of the Milky Way across the universe...

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  • $\begingroup$ I hadn't thought of that. The only thing is that it seems like they want an exact number, which would be too complicated in the answers you suggested. $\endgroup$
    – fay
    Feb 15, 2018 at 16:48
  • $\begingroup$ The first one would just be the circumference of the Earth divided by 2. $\endgroup$
    – F1Krazy
    Feb 15, 2018 at 16:50
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Or, how about

The man is on top of a mountain, walks 4 km down it (southwards), then enters a tunnel in the side of the mountain and walks 3 km down it (northwards).

enter image description here

Result: he is now many kilometers below the top of the mountain.

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my answer is

7 km

Because

If upon finishing his 4 km walk he is directly on the south pole, he can continue walking straight and be walking due north. Ending up, 7km from where he began.

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I have another answer, if they want a maximum distance.

39,930km, which would be the distance between his starting point and his ending point measured in the opposite direction of his travel, that, taking the polar circumference of the earth, and removing the 1km that a non-polar south-north walk would achieve.

However, if they're doing that, the answer could equally be

40,070km, which would be the likely equatorial distance perpendicular to his line of travel (assuming he started 500m north of the equator, and finished 500m south thereof).

But they're both nasty irrational answers, and I wouldn't countenance them personally.

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Obvious Answer:

7km - He starts 4km north of the South Pole and walks to it. All remaining paths are now due North and he chooses to walk the next 3km directly away from his starting point.

Of course,..

If he walks really slowly and we consider planetary rotation, orbit, galactic rotation, displacement through time, and the expansion of the universe, you could probably tack on at least 2 or 3 more km's to that. :-)

But my contribution is the following caveat. For my first answer or any other non-astronomical answer:

It depends entirely on the size of the planet.

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