A question I’ve heard several times in my life goes like this:
“A man walks 1 mile south, then 1 mile east, and then 1 mile north, and ends up on the same spot that he started. Where is he?”
The usual answer is the North Pole. However, there is also another answer that is any point on a circle about 1.15 miles north of the South Pole, which is not as obvious to most.
There’s an infinite set of circles near the South Pole that fit the constraint. If you’re about 1.08 mi from the pole, then you can go a mile south, wrap around twice, and then go north again. Or, if you’re 1.05 mi away, you can wrap around 3 times, etc.
It’s assumed that this occurs on earth. If the man is on a tiny asteroid or moon, the possibilities are endless.
I presumed they were talking about a filled in circle, so any point within it, not just on the cirumference. Would that work?
Edit: Also, here’s some unblurred text. Hopefully the context is clear that we’re discussing alternative answers to the south-east-north question.
Doesn’t work. You have to identify a circle with a circumference of precisely 1 mile, and then start on the circle one mile north of that. That way, when you travel 1 mile east on the inner circle, you end up on the same spot.
You can then identify inner circles of circumference 1/2 mile, 1/3 mile, 1/4 mile, and so on. You loop around more than once, but again if you travel exactly 1 mile east, you will end up at the same spot.
There are an infinite number of these circles, but they’re discrete–they don’t correspond to a filled-in circle.
I love NPR’s Sunday Puzzles. Recently there was one like this: think of a body part with seven letters. Add an N and rearrange the letters to get two body parts that aren’t related to the original one.
The intended answer–which I got–was “kneecap”, which can become “neck” and “nape.” But a lot of folks figured out that “N + asshole” could become “nose” and “lash.”
Will Shortz didn’t mention that alternate answer on the air. But I was reminded of a puzzle from many years ago: “Think of a five-letter word. Add a double-s to the word to make a seven-letter synonym of the word.” The intended answer was “bloom/blossom.” I though of a different answer, but didn’t send it in, because I’m not an a-hole.
I’m embarrassed how long it took me to figure out what part of the body a lash is.
When I saw the thread title, the first thing I thought of was Ken Jennings’ famous alternate answer on Jeopardy:
