### Games Interactive 2: Paint and Edges

Unexpectedly, I seem to have found a new technique for use in Paint by Numbers: eliminating possible positions for a run along an edge (either the natural edge of the grid, or any line past which you’ve eliminated any possibility of occupied squares) by considering how the perpendiculars affect the next tiers inward. For example, suppose the leftmost column in the grid says just “7”, and the column adjacent to it says “5”. It follows that the run of 7 must either have no rows in common with the 5, in which case it coincides with seven rows that start with 1, or have enough rows that begin with something other than 1 to accommodate the 5. That is, if you have seven rows that start with 1 except for one in the middle that starts with 2, that can’t be where the 7 goes, because it would place an isolated square into the second column where it can’t be part of the 5.

It’s obvious when you think about it. (If it doesn’t seem obvious from my description, my description is to blame. It would probably be clearer from an illustration.) But it’s a thing that’s easy to not think about, especially if you’re plugging away at the more usual techniques. The only thing that made me start thinking about it in this way was a sequence of puzzles that pretty much relied on this sort of reasoning, having lots of one-thick outlines around the edges.

I understand that popular logic puzzles, like nonograms and sudoku, have names for specific techniques. I don’t know the names, though, because I haven’t studied the theory. To me, finding the techniques yourself is part of the fun. Which I suppose marks me as a programmer.

Oh, yeah! That’s definitely one of my go-to techniques whenever I start a Paint by Number. In fact, after going through the first round of row-or-column-alone deciphering, I usually then start at the edges and work inward from there.