In Seoul Subway Line 2, subway stations are placed around a circular subway line. Assume that each segment of Seoul Subway Line 2 has a fixed price. Suppose that you hid money at each subway station so that the sum of the money is only enough for one roundtrip around Seoul Subway Line 2.
Prove that there is a station that you can start and take a roundtrip tour of Seoul Subway Line 2 while paying each segment by the money collected at visited stations.
The best solution was submitted by Kang, Dongyub (강동엽), 전산학과 2009학번. Congratulations!
Here is his Solution of Problem 2011-22. (typo in the lemma: replace an+i=an with an+i=ai.)
Alternative solutions were submitted by 서기원 (수리과학과 2009학번, +3 Alternative Solution), 장경석 (2011학번, +3), 김태호 (2011학번, +3), 김범수 (수리과학과 2010학번, +3), 박준하 (하나고등학교 2학년, +3).