Let \(A\) be an unbounded subset of the set \(\mathbb R\) of the real numbers. Let \(T\) be the set of all real numbers \(t\) such that \(\{tx-\lfloor tx\rfloor : x\in A\}\) is dense in \([0,1]\). Is \(T\) dense in \(\mathbb R\)?

The best solution was submitted by Kim, Kihyun (김기현, 수리과학과 2012학번). Congratulations!

Here is his solution of problem 2015-6.

Alternative solutions were submitted by 엄태현 (수리과학과 2012학번, +3), 이명재 (수리과학과 2012학번, +3), 이수철 (수리과학과 2012학번, +3), 이종원 (수리과학과 2014학번, +3), 정성진 (수리과학과 2013학번, +3), 최인혁 (2015학번, +3), 진우영 (수리과학과 2012학번, +3), 배형진 (마포고 1학년, +2). One incorrect solution was submitted (KDR).