Cosperdaghost, this is logical, the trick needed to prove the last four pixels is called the "mustache" or "smile" method, because it makes a smile shape in the end. If you try to put the "body" of the smile, if you will, all the way to one end, you end up with two pixels side by-side on the opposite end, and no space between them to satisfy the other row/column. It's sort of a two-step proof, but you eventually get to a point you can recognize it and don't need to use temporaries for it.
A lot of the time, Smiles end up in adjacent rows/columns, but as seen here, not always, sometimes they can be even farther apart, and no longer resemble that smile/mustache at all.