Combinatorics · Colouring arguments · Invariants · Trominoes · Constructions
Every cell of an \(n \times n\) table contains the number \(0\). One step consists of choosing three cells that form the shape
and adding \(1\) to each of the three numbers standing in them.
Can we, after finitely many steps, reach a table in which all the numbers are positive and equal to one another, when \(n = 3\)? And when \(n = 4\)?
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Slovenian High School Mathematics Competition for Vega Awards (MaSSA), drzavno (national) round 2012, 1. letnik, category A, problem 4. Organized by DMFA Slovenije (Society of Mathematicians, Physicists and Astronomers of Slovenia). Source