Working On My Knight Moves

Discrete Mathematics Level 3

Let \(f(x, y)\) return the number of places a knight can move to (in one move) on a standard \(8\times8\) chess board from the given \((x, y)\) position. What is the sum of \(f(x, y)\) for all \(x\) and \(y\)?

Here are some explicit examples:

  • \(f(0, 0) = 2\), \(f(5, 3) = 8\), \(f(7, 7) = 2\).
Inspired by Bob Seger's "Night Moves".
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Brock Brown by Brock Brown
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