The Stack

As promised, I spent much of the weekend on the two remaining Paint By Numbers sets, acutely aware as I did so that this is not the optimal use of my scant remaining hours upon this earth. But then, neither is whatever I would have been doing instead, so whatever. At this point, I’m pretty sure we’ve seen Games Interactive at its very worst and most grueling, and everything else will be relatively pleasant.

Let me talk a little about the process of solving Paint By Numbers puzzles. I usually get started by looking for rows and columns containing large numbers. In the extreme case, you have a run that fills its space entirely — say, you have a 25×25 puzzle and one of the rows is labeled “25”. That happened in one of the puzzles I just did, but it’s not common. More subtly, the numbers might leave only just enough space for a one-space gap between them, like if the same 25×25 puzzle has a row labeled “3 8 4 5 1”. The numbers add up to 21, plus four spaces between them. Most puzzles, however, don’t even have that, and have wiggle room even in their fullest rows. You can’t fill in the row entirely in that case, but you can often fill it in partially. Suppose you have a row “11 3”. If everything is in its leftmost possible position, the first number fills squares 1-11 and the second one 13-15. If everything is in its rightmost possible position, the second number fills 23-25 and the first 11-21. Since the first number fills square 11 in both its leftmost and rightmost positions, it fills it in all possible positions in between.

Once you have some stuff filled in, it starts acting as a constraint. The edges of the puzzle are particularly useful, because each square you fill in there nails down the position of a specific run immediately and absolutely. Any time you know the precise position of a run, it carves a space that must be unoccupied out of the perpendiculars at its boundaries, which can alter your analysis of what the leftmost and rightmost possible extents of things are. Often I wind up widening my area of certainty by one square, which allows me to be one square more certain in the other direction, and so on in a chain.

Now, this sort of logic can be frustratingly slow when you think you know what shape it’s making. It’s easy to say “Of course it’s symmetrical” or “It needs another leg” or whatever. But I prefer to stick to what I can reason out even then, because sometimes things aren’t quite the way you think they should be. They usually are, though, and people who let themselves fill in what they think is right probably wind up solving the puzzles a lot faster than me overall.

There is one situation where I tend to use my guesses about the picture, though: correcting mistakes. Sometimes I miscount something, or misread a number, or forget that I already have a square filled in at the opposite side of the puzzle, and I wind up with stuff that doesn’t fit together right. Unlike a lot of logic puzzles, I find I can usually recover from this without starting over completely. I just take one of the contradictory constraints and unravel it: Oh, so this is 10 squares long when the clue says 9? Let’s try erasing it on this end. That makes this other thing too short? Tack another square onto the other end. OK, but how did I decide which end to start with? Probably from my expectations of what the finished picture should look like.