Working On My Knight Moves

Probability Level 3

Let f(x,y)f(x, y) return the number of places a knight can move to (in one move) on a standard 8×88\times8 chess board from the given (x,y)(x, y) position. What is the sum of f(x,y)f(x, y) for all xx and yy?

Here are some explicit examples:

  • f(0,0)=2f(0, 0) = 2, f(5,3)=8f(5, 3) = 8, f(7,7)=2f(7, 7) = 2.

Inspired by Bob Seger's "Night Moves".

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