A discrete mathematics problem by Josh Rowley

Discrete Mathematics Level pending

Consider a standard \( 8\times8 \) chessboard. Define \( A \) as the maximum number of counters we can place on such a chessboard so that no 2 adjacent squares both have counters. Also, define \( B \) as the maximum number of counters we can place on such a chessboard so that no 2 squares which share a vertex both have counters. What is \( A + B \)?

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