Assume that a function \( f : (0, 1) \to [0, \infty) \) satisfies \( f(x) = 0 \) at all but countably many points \( x_1, x_2, \cdots \). Let \( y_n = f(x_n) \). Prove that, if \( \sum_{n=1}^{\infty} y_n < \infty \), then \( f \) is differentiable at some point.

The best solution was submitted by Jang, Kijoung (장기정, 수리과학과 2014학번). Congratulations!

Here is his solution of problem 2015-21.

Alternative solutions were submitted by 박성혁 (수리과학과 2014학번, +3), 이종원 (수리과학과 2014학번, +3), 최인혁 (2015학번, +3), 신준형 (2015학번, +2).