There is one thing I never do, never ever do, when I complete a Sudoku puzzle.

I never guess.

Sherlock Holmes famously said in The Sign of Four that a guess is “destructive to the logical faculty,” and I am not inclined to disagree. When it comes to Sudoku I puzzle it out, I think it through logically. I never put down a number until I am absolutely sure, even though that may mean that a puzzle will go unsolved.

I never guess.

Today, today I guessed.

On the train in the morning and evening, I will do the Sudoku puzzle printed in b, a local free daily paper. Usually, I’ll finish the puzzle on the train in the morning between State Center and Timonium, a ride of roughly twenty minutes. Sometimes, I’ll work on an unfinished puzzle on the evening train back home.

(Morning, I use a red pen, evenings blue. If I have to go back to the puzzle a third time, say on the subway out of town, I use black.)

This morning’s puzzle, in its early going, was simply, easy, perhaps deceptively so. As General Chang said, I was “lulled into a false sense of security.” The low-hanging fruit picked quickly, leaving behind more challenging fruits. I stared at the puzzle for whole minutes, stymied in my logical deductions, not putting down a single digit. All the tricks I knew came up short. I had the puzzle half done, I knew where certain numbers had to go, but I wasn’t sure. I couldn’t prove anything.

In one square of nine, I had five digits filled in. For the rest — the 2 could only go here or here, the 6 could only go here (overlapping with the 2) or here, the 1 and 8 could only go in the corners (overlapping with the 2 in one corner, overlapping with the 6 in another). I kept looking at this, and I reasoned. “If 2 goes here, then 6 goes here, and the Schrödinger’s 1 & 8 go here and here. Or, if 2 goes there, then 6 must go there, and the Schrödinger’s 1 & 8 must therefore go here and here.” I could not prove one state or the other; based on the solved state of the puzzle at that moment, both solutions to this nonant of the puzzle were correct. And even if I could place the 2 and the 6, I couldn’t solve the 1 and the 8; like Schrödinger’s Cat, these numbers were simultaneously in two states.

I wrote down “maps” of both solutions in the paper’s margin. I stared at them. I thought about them.

But there was nothing to think. I couldn’t prove anything. Either the first solution was true or the second solution was true, and one was as likely as the other.

I went with the second solution. I wrote down the 2. I wrote down the 6.

I couldn’t even say I had had an intuitive leap. All I could say, truthfully, was that I had made a guess.

And I never guess at Sudoku.

If my guess were wrong, I would know very soon. Numbers would double up somewhere. I would scrawl a giant “X” across the busted puzzle.

Instead, numbers kept falling into place.

In very short order, I had the puzzle solved.

All because of a guess. A 50/50 guess, but still a guess nonetheless.

I got lucky. I could so easily have gone for the other solution, and I would have ruined the puzzle irrevocably. Like Schrödinger’s Cat, the puzzle existed in a state of indeterminacy. Until I made a decision on the nonant, until I placed the numbers, the puzzle could not be solved. And like Schrödinger’s Cat, my very act of determining the numbers produced a result — the puzzle could live (and be thus solved) or die (and be thus busted), but unless I acted, I would never know. The uncertainty had to be broken down.

I never guess.

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