What to do instead of guessing

Guessing is the move every Sudoku solver is tempted by at some point — usually about twelve minutes into a hard puzzle, with two or three cells left that all look equally constrained. The temptation is rational: the guess is fifty-fifty, you'll know within thirty seconds whether it worked, and if it didn't you'll have made progress through elimination.

The temptation is also wrong, in a specific and useful way. Sudoku is a logic puzzle, which means every cell has exactly one digit that can go in it — provable from the rules without ever guessing. If you're tempted to guess, the puzzle is telling you something about the technique you haven't found yet, not about how lucky you're feeling.

What guessing actually does to the puzzle

A guess collapses the puzzle into trial and error. If the guess is right, you've made one of the moves you would have made anyway, but you've made it without knowing why. If the guess is wrong, you've placed a digit that conflicts with the rules, and you've now committed to either tracking back to the moment of the wrong guess (potentially many moves later) or restarting the puzzle entirely.

Both outcomes are worse than they sound. The right-guess outcome trains your brain to skip the technique that would have found the move logically — which means you'll find that move slower the next time you encounter it. The wrong-guess outcome trains your brain to associate "stuck on a hard puzzle" with "give up and restart" rather than with "find the technique." Both habits are corrosive to your puzzling.

The cleaner alternative — finding the move you can't see — preserves both the puzzle's integrity and yours.

What stuck actually means

"Stuck" in Sudoku usually means one of three specific things, and recognising which is the first step toward un-stuck:

1. You've solved everything that's solvable with the techniques you currently know. This is the most common stuck. The puzzle requires a technique you haven't learned (or haven't fully internalised), and the rest of the grid is patiently waiting for you to find it.
2. You have the technique but you're applying it to the wrong region. Pointing pairs are visible in some boxes and not others; X-wings exist in some rows and not others. If you've scanned the obvious places without success, the move is hiding in a place you haven't scanned.
3. You've made a mistake somewhere earlier and the puzzle has become unsolvable. Less common, but it happens — particularly if you've been pencil-marking aggressively. A bad pencil mark from twenty cells ago can compound into an apparent dead end.

The diagnostic: which of these is your stuck? You can usually tell within thirty seconds of looking at the grid carefully.

Things to try before guessing

Before reaching for a guess, work through this short list:

• Re-scan with the digit you've placed least. A digit that's been placed only twice usually has the strongest constraints on its remaining homes. Find them.
• Look for naked or hidden pairs. Two cells in the same unit that share the same two candidates — the rest of the unit can't contain those candidates. Easy to miss, often the unlock.
• Check pointing pairs. When two of a digit's candidates in a box sit in the same row or column, the digit can't appear elsewhere in that row or column outside the box.
• Try a fresh look at the most-pencil-marked region. The cluster with the most candidates is often where the pattern is hiding; over-marking can hide it.
• Walk away for sixty seconds. Sometimes the technique surfaces on a second look that wouldn't on a long stare.

Most stuck moments resolve to one of the items above. The technique you don't have yet has a name (and we'll write the encyclopedia entries for those in a later session); most of the time, though, the technique you do have is the one that breaks the puzzle — you just need to apply it where you haven't looked yet.

When restart is honestly the better move

If you've been at the same puzzle for thirty minutes, you've worked through every technique you know, and you've checked your pencil marks for errors and found none — sometimes the puzzle has slipped past your current skill level, and the best move is to start fresh on an easier difficulty.

There's no shame in this. A hard puzzle that you can't quite solve today is one you'll come back to in a month with another technique under your belt and finish in five minutes. Restart on easy or medium, finish a satisfying puzzle, and put the hard one aside until your toolkit grows.

The bottom line

Don't guess. The puzzle has a technique waiting for you, even when it doesn't feel like it does. The list above will resolve most stuck moments. Patience and a wider scanning habit will resolve most of the rest. And when all else fails, restart on something easier — tomorrow's puzzles will still be there.