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Thanks to Hyeong-jun (H. J.) for emailing me this problem! This is a challenging problem from the math section of the 1997 CSAT, a standardized test in South Korea. Can you figure it out? It took me several attempts, but it was really satisfying when I solved it (I did need to look up one key insight, which is the first thing presented in the solution). So give it a try, and don't peek at the rest of the solution too early!
0:00 Problem
1:58 My many attempts
3:28 Unwrapping a cone
5:14 Solution
Coordinate geometry solution and proof of uphill/downhill track
www.desmos.com/calculator/l18...
Note: pretty much every time I said or wrote "circular arc" I meant to say or write "circular sector." A "circular arc" is a portion of a circle's circumference; a "circular sector" is the enclosed region between the arc and two radii.
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"Math Puzzles Volume 1" features classic brain teasers and riddles with complete solutions for problems in counting, geometry, probability, and game theory. Volume 1 is rated 4.4/5 stars on 13 reviews.
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