For example, in the diagram
all entries can be filled by completing rows, columns or boxes that have 8 entries filled already and only miss the last entry.
Indeed, the upper left hand box, and the upper right hand box, and the middle left hand box, and rows 1, 2 and 4, and columns 2, 3 and 8 can be completed immediately. This yields the diagram
Now also row 3 and column 6 and the lower left hand box can be filled, and we have
Next we can fill the bottom two rows, and column 5, and the middle bottom box. That yields
Finally we can fill the middle box and the lower right hand box, and then column 9, and then rows 5, 6. That completes the sudoku.
Mathematical Note Check that the rank of the system of equations is 21, so that one cannot fill more than 21 empty positions using baby steps only.
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