INMO 2025 Questions, Solutions, Discussions

(INMO 2025 P5, AoPS, proposed by Pranjal Srivastava and Rohan Goyal) Greedy goblin Griphook has a regular \(2000\)-gon, whose every vertex has a single coin. In a move, he chooses a vertex, removes one coin each from the two adjacent vertices, and adds one coin to the chosen vertex, keeping the remaining coin for himself. He can only make such a move if both adjacent vertices have at least one coin. Griphook stops only when he cannot make any more moves. What is the maximum and minimum number of coins that he could have collected?