2023 SSMO Team Round Problems/Problem 9

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Problem

Let $B$, $K$, and $R$ be the total number of possible moves for a bishop, knight, or rook from any position of a $9$ by $9$ grid. Find $B + K + R$.

(A bishop moves along diagonals, a rook moves along rows, and a knight moves in the form of a $2 \times 1$ "L" shape)

Solution