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2011 AMC 12A Problem 2

Problem 2 of 25Easier

There are 55 coins placed flat on a table according to the figure. What is the order of the coins from top to bottom?

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Solution

Coin CC is drawn as a complete, unbroken circle, so nothing covers it and it lies on top. Reading the remaining overlaps, each coin’s uncovered arc shows it sits above the next: CC covers E,E, EE covers D,D, DD covers B,B, and AA covers BB while lying under the others. This gives the top-to-bottom order (C,E,D,A,B).(C, E, D, A, B). Thus, the correct answer is E.

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Concepts: logical deduction

Problem text and solution from the LIVE past-contest archive. See also the AoPS wiki page for community solutions.