Prove that for any given positive integer \( n \), there exists a sequence of the following operations that transforms \( n \) to a single-digit number (in decimal representation).

1) multiply a given positive integer by any positive integer.

2) remove all zeros in the decimal representation of a given positive integer.

The best solution was submitted by 강한필 (전산학부 2016학번, +4). Congratulations!

Here is his solution of problem 2021-01.

Other solutions was submitted by 김기수 (수리과학과 2018학번), 박은아 (수리과학과 2015학번, +3), 전해구 (기계공학과 졸업생).