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This question already has an answer here:

Here is another puzzle:

The year is 1895 and subaltern Henry Faversham, of the British army, is being interviewed by Maude Muckraker for the Independent London Times. It looks as if Maude is having her doubts about the yarn young Henry is spinning. He claims that on a recent hike his outfit, starting at some undisclosed part of the world, marched due south for 100 miles, then due east for 200 miles, turned once again and marched due north for 100 miles and ended up back where it had started from.

"Impossible", snorts Maude, terminating the interview. "What is your claim, young man, is patently impossible!"

Is Maude wrong, or is there a spot on earth where Henry could have carried out this march? Can you tell us where this exotic place is located?

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marked as duplicate by F1Krazy, Community Feb 5 '18 at 16:14

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In addition to the North Pole, he could also have started anywhere on a circle with radius 100+(200/2pi) miles from the South Pole.

Note that for completeness, the South Pole distance is actually 100+(200/(2*k*pi)) miles, where k is any integer, such that walking 200 miles would complete k complete circles around the pole.

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  • $\begingroup$ Of course nobody reached the north pole until the 20th century so Henry's story being told in 1895 is indeed highly suspect. Similarly the first person to the south pole was also in the twentieth century. Funnily enough it is much harder to find evidence of when the first person got to within 60 miles of the south pole but I would be surprised if anybody got that close in 1895. I would also be fairly sure that the British Army didn't have men stationed in that area so on the whole while there is an area that it is theoretically possible it is also extremely doubtful... :) $\endgroup$ – Chris Feb 5 '18 at 16:38
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Well known puzzle, he was

On the north pole.

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