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As Inefficient As Possible

Source: Indonesia RMO 2022, Essay No 5 (Modified from Mathematical Excalibur 510)

August 24, 2022
IndonesiaRMO2022mathematicalexcaliburcombinatorics

Problem Statement

Numbers 11 to 2222 are written on a board. A "move" is a procedure of picking two numbers a,ba,b on the board such that b≥a+2b \geq a+2, then erasing aa and bb to be replaced with a+1a+1 and b−1b-1. Determine the maximum possible number of moves that can be done on the board.
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