COINCIDENT EQUATIONS. Here is a progress report on the Sudoko solver. First, change all the equations shown here to have 45 (sum nine, not ten) as the known value of a row, column, or submatrix. Second, recall the nasty properties of a singular matrix. A problem that frequently crops up in solving a Sudoku is that the two remaining numbers of a submatrix occupy the same row or column of the submatrix. If the rest of your work is correct, the sum of the missing values will be equal to 45 less the summed known values within the submatrix which will be the same as 45 less the summed known values within that row or column. (If they're not the same, that's a warning to check the rest of your work.)

There are also developments on the transformation and transposition properties of these puzzles. More anon.