Let \( n \) be a positive integer. Determine all continuous functions \(f: [0, 1] \to \mathbb{R}\) such that
\[
f(x_1) + \dots + f(x_n) =1
\]
for all \( x_1, \dots, x_n \in [0, 1] \) satisfying \( x_1 + \dots + x_n = 1\).

The best solution was submitted by 김유일 (2020학번) Congratulations!

Here is his solution of problem 2020-19.

Other solutions was submitted by 길현준 (수리과학과 2018학번, +3), 채지석 (수리과학과 2016학번, +3), 이준호 (수리과학과 2016학번, +2).