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.