Daily Archives: May 1, 2015

2015-8 all lines

Does there exist a subset \(A\) of \(\mathbb{R}^2\) such that \( \lvert A\cap L\rvert=2\) for every straight line \(L\)?

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Solution: 2015-7 Binomial Identity

Prove or disprove that \[ \sum_{i=0}^r (-1)^i \binom{i+k}{k} \binom{n}{r-i} = \binom{n-k-1}{r}\] if \(k, r\) are non-negative integers and \(0\le r\le n-k-1\).

The best solution was submitted by Chin, Wooyoung (진우영, 수리과학과 2012학번). Congratulations!

Here is his solution of problem 2015-7.

Alternative solutions were submitted by 고경훈 (2015학번, +3), 김기현 (수리과학과 2012학번, +3), 박훈민 (수리과학과 2013학번, +3), 엄태현 (수리과학과 2012학번, +3), 오동우 (2015학번, +3), 윤준기 (수리과학과 2014학번, +3), 이수철 (수리과학과 2012학번, +3), 이영민 (수리과학과 2012학번, +3), 이종원 (수리과학과 2014학번, +3), 정성진 (수리과학과 2013학번, +3), 최인혁 (2015학번, +3), 함도규 (2015학번, +3), 김성민 (캠브리지대학 진학 예정, +3).

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