The Stack

As before, Paint by Numbers is weekend work. The game has six sets. I’ve done two so far, and expect to manage a third today, leaving the other half for next week. The palette this time is missing the dithered grey that I previously used to mark uncertain squares, so I’ve been using yellow for that purpose instead. At least the two-semantically-distinct-whites problem is gone.

The chief characteristic of Paint by Numbers is that it’s methodical. I described the basic solving process in a previous post: you look for a thing that just barely fits in the space available, which gives you information about its position, which imposes constraints on other things, and so on. It takes time, but you can keep on extending the chain of logic for as long as you keep finding leads. Every once in a while, though, the chain seems to end. Maybe you reach a point where the necessary reasoning takes more steps before yielding concrete results. Maybe there really is a simple next step, but it’s hard to spot. Either way, I wind up marking, in a different color, the things that I suspect rather than just the things that I know.

I don’t like taking this step, because it seems so much less certain than the plodding and methodical reasoning. But is it really? In theory, logic should never steer you wrong, but it’s being applied by a fallible human mind. I frequently do make mistakes. Occasionally, I even make mistakes so severe that I have to correct them by wiping the entire grid and starting over. Intuition may well be a better guide, especially as I train it up by solving these things. It would certainly be faster. I remember struggling with anagrams in crosswords as a child, seeing no good way to solve them other than by writing down every possible arrangement of letters to the point where they stopped making sense. Nowadays, all I usually have to do is look at the letters and, if I have enough constraint from the cross-letters and clue, the solution just pops out at me unbidden. Could a human mind get to the point of solving nonograms the same way? I suspect so, given the prodigious mental feats that “Human Calculators” have trained themselves to do. Heck, after all this intensive practice, I may well be closer to that point than I’ve been allowing myself to acknowledge.