Perhaps obvious and common knowledge, yet apparent to myself only after some thought, is the distribution of values in a successful game of Sudoku.
Using a Sudoku game board of uniform squares arranged with symmetry, the xy origin is established at the center of cell r5 c5. When wholly populated, each cell’s center is assigned a mass of magnitude equal to its respective numeric value. The resulting center of gravity for the matrix is found to be coincident with the origin (Fig. 1). This from:
The same methodology can be applied to each 3 x 3 sub grid finding local center of gravity’s and then the global value from the nine (Fig. 2).
As well again, the same applied to cells of common radius from the origin where r has been calculated for each (Fig. 3) from:
Center of gravity values for the fourteen concentric rings can then be consolidated to yield the overall. Knowing convergence at r5 c5 is requisite for success, plotting (Fig 4. & 5.) the center for gravity’s path from a starting partial population through the subsequent filling of cells may provide game strategy and solution analysis.
