Dragomir Grozev
Institute of Mathematics and Informatics
Bulgarian Academy of Sciences - Sofia
https://doi.org/10.53656/math2024-6-1-ont
Absract. The article is dedicated to solving Problem 3 from the International Mathematical Olympiad (IMO) 2024. The wording looks deceptively easy, but the problem turned out to be quite difficult for many of the participants, including the Bulgarian contestants. We interpret the process as an infinite path in a directed graph, which
allows us to more easily prove the key claims.
Keywords: infinite sequence; periodic sequence; directed graph; infinite path
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