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A lost and hungry traveller, who was particularly known to be much better suited for travelling by sea than air, spent a good part of one long night relentlessly heading straight south for 400 miles. At which point, he began hearing strange sounds and spotted a very distant and unfamiliar flag.

Ever curious, but wanting to avoid any confrontation, he turned right to move straight west for 20 miles, then made a second right to head straight north again for another 400 miles. At which point he arrived right back where he'd began that night.

Who was the traveller? Where was he travelling? What flag did he see?

Small hint

A map or regional knowledge may be required.

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  • $\begingroup$ Not a duplicate. $\endgroup$ – RobStone Aug 19 '16 at 14:42
  • $\begingroup$ Consider this one a trickier extention perhaps. $\endgroup$ – RobStone Aug 19 '16 at 14:43
  • $\begingroup$ which is why I linked it as a related question for future readers rather than flag it as a duplicate $\endgroup$ – kaine Aug 19 '16 at 14:45
  • $\begingroup$ How accurate are your measurements? Is it exactly 400 miles, or could it be 436 miles? $\endgroup$ – Chris Cudmore Aug 19 '16 at 15:51
  • $\begingroup$ 400-500? I didn't measure exactly. The location is ambiguous to any degree $\endgroup$ – RobStone Aug 19 '16 at 15:53
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The traveller is

a penguin! A much better swimmer than flyer.

He saw the flag of

The United States of America. There's one at the Amundsen-Scott South Pole Station.

He started out

about 403 miles from the south pole. Actually, 400 + 20/2pi, because he walked south 400 miles, to a spot where he could see the Amundsen-Scott South Pole Station about 3 miles away. He walked in a complete circle around it. This circle happened to be 20 miles in circumference.

Then he headed north 400 miles to get back where he started.

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    $\begingroup$ Is there any particular reason the traveller needs to be the one you described? Technically it could be anyone? $\endgroup$ – yitzih Aug 19 '16 at 16:23
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    $\begingroup$ @yitzih "who was particularly known to be much better suited for travelling by sea than air," $\endgroup$ – Chris Cudmore Aug 19 '16 at 16:26
  • $\begingroup$ I suppose it acts as a riddle here. Possibly an unfair hint to future readers, but the traveller would be able to survive this trip. The rest of the clues in context might eliminate most other options. $\endgroup$ – RobStone Aug 19 '16 at 16:34
  • $\begingroup$ Must have mighty good eyes to see a flag at 3 miles away. Maybe instead he started at 400.01 miles away from the flag, and made several "laps" instead of just one. $\endgroup$ – Keeta - reinstate Monica Aug 19 '16 at 19:08
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Am I a

Ray?

Because

Most Internet connections travel by optical sea cables (suited), some is satellite transmitted. A ray produces raises what is commonly known as a error code 400 flag for bad request, which happens during a lot of traffic (noise in this context).

The flag he saw was

HTTP error 400

Where was he travelling?

To the website hosting server of course, from where the Ray took a u turn and came back to the client terminal.

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  • $\begingroup$ (You only need 1 > for a spoiler) $\endgroup$ – Beastly Gerbil Aug 19 '16 at 15:19
  • $\begingroup$ I like your guess, but it's not correct. $\endgroup$ – RobStone Aug 19 '16 at 15:55
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The traveller might be

an icebear. Starting from the North Pole, he might have reached Greenland, Canada or maybe even Iceland before turning West, so the flag is probably one of those countries.

As an alternative, the traveller might start from a little bit more than 400 miles north from the South Pole. He almost reaches the Pole before turning to West, where he makes a full circle (or more circles) around the Pole on a latitudinal circle, then he turns back to North. The flag he sees might be a Norwegian one left at the pole by Amundsen.

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  • $\begingroup$ A rather good guess, but not what I'd had in mind. Recently updated for a more accurate story. $\endgroup$ – RobStone Aug 19 '16 at 14:08
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Think about a circle that is 20 miles in circumference, and just north of the South Pole. We’ll call that C(1).

If you are 400 miles north of this circle, then you will also end up back at the same spot. You will travel one mile south, then you’ll travel one mile around the circle, and then you’ll go north and end up back at the same spot as you started.

Actually this is true for any point on the circle that is 400 miles north of C(1). So this is an infinite number of solutions.

Infinity times infinity!

Now think about a circle that is 10 miles in circumference and also just north of the South Pole. We’ll call that C(1/2).

If you are 400 mile north of this circle, then you will also end up back at the same spot. You will travel 400 miles south, then you’ll travel the circle TWICE, and then you’ll go north and end up back at the same spot.

Similarly, if you are 400 miles north of the circle C(1/3)–a circumference of 1/3 near the South Pole–then you will also end up back at the same spot. You will travel around C(1/3) a total of 3 times.

We can use the same argument for C(1/4), C(1/5), and so on for any C(1/n), where each circle has a circumference of 1/n. If you go one mile west in any of these circles, you will travel around the circle n times and end up back at the same point.

Therefore, you will always end up at the same spot if you are one mile north of any circle C(1), C(1/2), C(1/3), etc.

There are an infinite number of C(1/n) circles, and you can be anywhere on the circle one mile north of each circle.

So this is basically infinity times infinity points.

In conclusion

The complete solution is you can be:
400 miles north of C(1) (infinity points)
400 miles north of C(1/2) (infinity points)
400 miles north of C(1/3) (infinity points)
…
400 miles north of C(1/n) (infinity points)
…

So this is basically 1 + (infinity)(infinity).

It’s a great question! however with regards to the flag i have no idea.

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  • $\begingroup$ Nice logic, but it doesn't really answer the question. $\endgroup$ – Mithical Aug 19 '16 at 14:50
  • $\begingroup$ I'm aware. the point of the answer is to say he/she/it could be anywhere from 400 miles north of the south pole to 400 miles north of a 20 mile circumference north of the south pole on any longitude.. I'm fairly sure the destination it wanted to reach was the south pole and would have been a penguin but still no idea on the flag. $\endgroup$ – c.pullen Aug 19 '16 at 14:58
  • $\begingroup$ See puzzling.stackexchange.com/help/how-to-answer $\endgroup$ – Mithical Aug 19 '16 at 15:00
  • $\begingroup$ I'm not sure why you have pointed me to there... i've read through it and ive done pretty much everything applicable $\endgroup$ – c.pullen Aug 19 '16 at 15:10
  • $\begingroup$ Because I still don't think it answers the question... :/ $\endgroup$ – Mithical Aug 19 '16 at 15:13
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The south/west/north travel suggests someone starting from

The north pole

As they're better suited to travelling by sea than by air, might they be

A narwhal? It could have swam far enough south to see either a Canadian or Greenland(-ian?) flag, both countries that have historically hunted it
Given the strange noise, chances are it came across an expedition to the north pole. The most distant (read: Southern) one I can find is a Shinji Kazama from Japan, who travelled there by motorcycle. Assuming he started from northern Greenland or Canada (at least 400 miles), a Japanese flag would indeed be a 'very distant and unfamiliar' one

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  • $\begingroup$ This would seem plausible, but it doesn't lead you to identify a flag? $\endgroup$ – RobStone Aug 19 '16 at 14:28

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