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The Math Less Traveled 
For the grid in row r and column c, it looks like the numbers, n, which exist are filled in indices corresponding to the sequence (n +1 mod r,n + 1 mod c). I don’t know about the empty squares.
Pingback: A few words about PWW #25 | The Math Less Traveled
Pingback: More words about PWW #25: The Chinese Remainder Theorem | The Math Less Traveled
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