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A man decides to go on a long jorney. From his house he goes exactly 90 miles south, then 90 miles west, then 90 miles north. He is now back at his house. How is this possible.

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... in the Northern hemisphere.

Start at the North Pole.

... in the Southern hemisphere.

1. Start 90 miles north of a latitude line that constitutes a 90-mile circumference circle. - i.e. 90 + 90/2pi miles north of the South Pole.

2. Start 90 miles north of a latitude line that constitutes a 90/2-mile circle. - i.e. 90 + 90/4pi miles north of the South Pole.

...

N. Start 90 miles north of a latitude line that constitutes a 90/N- mile circle. - i.e. 90 + 90/2Npi miles north of the South Pole.

...

Keep inching south approaching but never reaching a point 90 miles north of the South Pole.

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his house is a mobile home, and someone moved it while he was travelling on his long journey...

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... in the Northern hemisphere.

Start at the North Pole.

... in the Southern hemisphere.

1. Start 90 miles north of a latitude line that constitutes a 90-mile circumference circle. - i.e. 90 + 90/2pi miles north of the South Pole.

2. Start 90 miles north of a latitude line that constitutes a 90/2-mile circle. - i.e. 90 + 90/4pi miles north of the South Pole.

...

N. Start 90 miles north of a latitude line that constitutes a 90/N- mile circle. - i.e. 90 + 90/2Npi miles north of the South Pole.

...

Keep inching south approaching but never reaching a point 90 miles north of the South Pole.

That's sweet. It took a bit to wrap my head around it, but once it clicked I wished I'd thought of it. I look forward to reusing that explanation.

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