## Problem of the Day #380: Filling a Grid, Part II
*April 2, 2012*

*Posted by Alex in : potd , trackback*

Given a grid with $R$ rows and $C$ columns, what is the maximum number of cells that can be colored such that no colored cell is adjacent to more than $X$ other colored cells? Solve the problem for $X = 0, 1, 2, 3$ and express your answer in terms of $R$ and $C$. Two cells are adjacent if they share an edge.

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