Ephemeral

Every morning I open up a book of 3000 Sudoku puzzles and task away at one or more with my morning coffee. Unlike online sudoku, because it’s in a book, there is no feedback system for if I write a wrong number in a wrong slot. This means I can merrily make the wrong decision and go trotting down the 9×9 squares getting *everything wrong*, sometimes for a good chunk of the puzzle (more than 50%), before realizing I made a wrong choice *somewhere* previously and have to erase and start over.

Of course, I don’t have to actually erase and start over. I could strategically walk through every number choice, working painfully through the puzzle and pseudo-marking the *right* choices in an attempt to disambiguate them from an *unproven/wrong* choice, effectively re-working the puzzle but with a lot more noise. OR I can pull out my trusty Pentel Eraser and just axe the whole thing, with the faintest traces left on the page, and start (mostly) fresh.

There are pros and cons to each approach: the painstaking way forces me to find very, very specifically where I chose wrong, but it takes longer and is prone to confusion from previous choices. The quicker way gets me to the overall solution faster but means re-applying numbers that were good in the first place. Either way I’m giving something up: time, or effort.

One way is not “better than” the other, in the sense that sometimes wholesale erasure and restarting is important (in the case of Sudoku, this can be when you are on a fixed timeline and you have to Go Do A Thing shortly and you want the puzzle Done before you Go Do The Thing and you’ll take your lesson later) and sometimes strategic walk through is important (in the case of Sudoku, this can be when you are making the same mistake over and over and need to figure out *why*). (The very worst approach is to start off the painstaking way, decide it’s too hard, and then erase — you’ve wasted time and aren’t getting the benefit of the investment).

What is true in both cases is the problem is ephemeral and can be solved: I just have to choose my method and then stick with it. I’ve already sunk the cost of my initial investment in the puzzle, and if I choose to parse through the individual choices to find *why*, or if I choose to erase and start over, nothing is bringing back that initial time investment.

With Sudoku, I almost always choose the “erase and start fresh” method, for two reasons: I typically don’t have enough time in the morning to re-parse through my choices, and, it’s of dubious benefit if I do: the fact that there are 3,000 *different* Sudoku puzzles in this book alone tells me that parsing through my wrong choice in *this one* will probably not tell me anything useful for the next one, on a per-puzzle basis. Per this article I get about 5.5 billion combinations and that is more than I will ever do in my lifetime (I have roughly 40-45 years left and if I did 5 a day every day for that period I have maybe 82 thousand puzzles left to do). (Hyperbole: I’d have to do about 335k puzzles/day to get them all done before I die. #goals).

But if it’s a *trend* — If I consistently find myself getting it wrong, over and over, it’s less about the puzzle and it’s more about me: am I constantly making assumptions about something? Am I not really paying attention? If it’s important enough to understand why, there are times when picking through the choices are valid: oh, I made an assumption about X number being in N place when I had no data for that. Or, oh, I conflated that number with this number (e.g., looking at the trend of 3’s in the blocks and then misapplying it to a different number/relationship). That won’t help me get through the block sooner but it will help me understand why I’m messing up and that maybe it’s time for coffee or a break.

I work (perhaps unsurprisingly) in engineering, and almost always the faster way of dealing with a problem is to start over. Sometimes you get to carve in some things that you *know* are good — in Sudoku this would be the numbers that are prepopulated for you and maybe your first four moves — and then you go from there. Generally speaking, as long as everyone’s ok with that approach (in any industry you can have things cheaply, quickly, and of good quality: pick two), that is the way to go. “Starting over” is expensive but may be cheaper than “refactoring extant” (the assumption here is that quality is not up for grabs). What you sacrifice is the inability to really hyper specifically target how you got into a specific pickle, which, sometimes you need. Sometimes, though, it’s enough to know you got there… and to work more diligently and specifically to ensure you don’t go back.