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Omni-MATH / Let n be the maximum number of bishops that can be placed on the squares of a 6×6 chessboard such that no two bishops are attacking each other. Let k be the number of ways to put n…

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problem

Let nn be the maximum number of bishops that can be placed on the squares of a 6×66 \times 6 chessboard such that no two bishops are attacking each other. Let kk be the number of ways to put nn bishops on an 6×66 \times 6 chessboard such that no two bishops are attacking each other. Find n+kn+k. (Two bishops are considered to be attacking each other if they lie on the same diagonal. Equivalently, if we label the squares with coordinates (x,y)(x, y), with 1≤x,y≤61 \leq x, y \leq 6, then the bishops on (a,b)(a, b) and (c,d)(c, d) are attacking each other if and only if |a−c|=|b−d||a-c|=|b-d|.)
Plain-text mathematical notation (without MathML)
Let n be the maximum number of bishops that can be placed on the squares of a 6×6 chessboard such that no two bishops are attacking each other. Let k be the number of ways to put n bishops on an 6×6 chessboard such that no two bishops are attacking each other. Find n+k. (Two bishops are considered to be attacking each other if they lie on the same diagonal. Equivalently, if we label the squares with coordinates (x,y), with 1≤x,y≤6, then the bishops on (a,b) and (c,d) are attacking each other if and only if |a−c|=|b−d|.)
Original LaTeX notation
Let $n$ be the maximum number of bishops that can be placed on the squares of a $6 \times 6$ chessboard such that no two bishops are attacking each other. Let $k$ be the number of ways to put $n$ bishops on an $6 \times 6$ chessboard such that no two bishops are attacking each other. Find $n+k$. (Two bishops are considered to be attacking each other if they lie on the same diagonal. Equivalently, if we label the squares with coordinates $(x, y)$, with $1 \leq x, y \leq 6$, then the bishops on $(a, b)$ and $(c, d)$ are attacking each other if and only if $|a-c|=|b-d|$.)

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task_id
53ea4b29-d8ac-522e-ae68-1f9fd62841a2
task_key
test--53ea4b29-d8ac-522e-ae68-1f9fd62841a2
task_revision_id
1
config / split
/ test

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