Every sudoku player hits the moment: twenty squares left, no obvious move, and a square with two pencil marks that looks like a coin toss. Do you have to guess? Or did you miss something?

We wanted a number instead of a shrug, so we dealt 3,000 puzzles at each level of our Sudoku, 12,000 in all, and solved every one with a program that is only allowed to use named human techniques. It never guesses. For each puzzle we asked two things: does it have exactly one answer, and what is the hardest technique you cannot do without?

The short answer

  • Every one of the 12,000 had exactly one solution. A separate brute-force counter checked this, and found the same answer as the game.
  • Every one was finished by logic alone. 11,812 of them (98.4%) fell to pattern techniques. The other 188, all Expert, needed a forcing chain: a structured "what if" that we explain below. None needed a blind guess.
  • On Easy, Medium and Hard you never need to guess or even try a what-if. If you are stuck on one of those, there is a move you have not spotted yet.

Every move our solver made was checked against the real solution while it ran: not one placement or crossed-out pencil mark was wrong.

This is about our puzzles. Sudokus from newspapers and other apps may be built differently, and there are valid one-answer sudokus that no named human technique can crack. So "no sudoku ever needs a guess" is not true; "none of ours did" is.

What each level actually demands

"Needs" here means something strict. We gave the solver a ladder of techniques, simplest first, and found the shortest stretch of that ladder that finishes the puzzle. The top rung of that stretch is the technique the puzzle cannot be solved without; take it away and the solver stalls. (Why we rate this way and not by what happens to get used is in Rate a puzzle by what breaks without it.)

Easy: naked singles, 100%

All 3,000 Easy puzzles fall to the most basic move there is: a square where only one digit can go. You never need anything else.

Medium: hidden singles, 100%

All 3,000 needed the hidden single: a digit that has only one square left in its row, column or box. Naked singles alone stall on every one. This is the whole jump from Easy to Medium. If Medium feels hard, scan one digit at a time across the grid instead of staring at one square.

Hard: pointing and claiming, then naked pairs

  • 78.2% needed pointing or claiming (both explained on the Sudoku rules and strategy page) and nothing harder.
  • 21.5% stalled even with pointing and claiming, and needed a naked pair.
  • 0.4% (11 puzzles) turned out to need only hidden singles. The generator has 24 tries to hit the Hard band, and very rarely it misses and hands you the closest it got.

So if you are moving up to Hard, pointing and claiming is the one to learn.

Expert: past the basics, every time

All 3,000 Expert puzzles stall once singles, pointing, claiming and naked pairs run out. The game's own rater, written separately from ours, agreed on all 3,000. Here is what they needed instead, grouped:

  • 6.5%: a hidden pair, or a triple or quad. A hidden pair is two digits that can only go in the same two squares of a row, column or box, so those squares can lose every other pencil mark.
  • 17.5%: a wing or a fish. Mostly the XY-Wing (14.7% on its own): three squares with two pencil marks each, arranged so that whichever way the middle one goes, one of the outer two holds a shared digit, so any square that sees both outer squares cannot. X-Wing, Swordfish and XYZ-Wing make up the rest.
  • 69.7%: a chain. A chain follows "if this is not here, then that must be there" from square to square. An X-Chain follows a single digit (21.0%), an XY-Chain hops between two-candidate squares (23.1%), and a full alternating inference chain mixes both kinds of link (25.6%).
  • 6.3%: a forcing chain. Take one square (or one digit's possible places in a row, column or box), try each option in turn, follow only the singles each one produces, and keep whatever every option agrees on (3.6%). In the hardest 2.7%, one option runs into an impossible grid within those singles, so you cross it out.

That last 2.7% is the honest edge of "no guessing". Trying an option and watching it break is close to a guess, but it is a short, checked one: you follow singles only, and you never write in a digit you are not sure of. Not one of the 12,000 needed the real thing, which is picking a digit, carrying on for twenty moves and hoping.

What makes a sudoku hard

It is not the number of clues. Our Medium puzzles started with anywhere from 23 to 40 clues, and our Hard ones from 21 to 37. A 23-clue Medium needed nothing harder than a hidden single, while a 37-clue Hard still needed pointing and claiming. The difficulty is the hardest step the puzzle forces on you, not how empty the grid looks.

So the way to move up a level is to learn one technique, not to get faster:

  • Easy to Medium: hidden singles.
  • Medium to Hard: pointing and claiming, then naked pairs.
  • Hard to Expert: hidden pairs and the XY-Wing first. About a quarter of Expert puzzles (24.0%) need nothing past pairs, triples, wings and fish. The rest need chains, so learn the X-Chain next.

So, do you have to guess?

On our Easy, Medium and Hard puzzles, never. On Expert, nearly never: 93.7% need no what-if at all, and the rest need a short, checkable one. If you are stuck, you have almost certainly missed a deduction, not reached a coin toss.

Play Sudoku free: four difficulties, a daily puzzle and no account. If you want sudoku logic with sums added, try Killer Sudoku. And for a game where guessing really is part of it, see Is Minesweeper luck?