How to Solve Sudoku Without Guessing

Why people end up guessing

Almost everyone learns sudoku the same way: look for an obvious number, write it in, look again. On easy puzzles the obvious numbers keep coming. On harder ones they dry up, and the board turns into a fog of half-remembered possibilities. At that point the only moves left seem to be “try a 3 here and see what happens” — and when that goes wrong, the error can sit undetected for twenty moves.

The fix is not a cleverer trick. It’s a different way of collecting information, so that you never run out of it.

Step 1 — Think in digits, not cells

Instead of staring at one empty cell and asking what could go there, pick a digit and ask where it can still go across the whole board. Start with 1. For each 3×3 box that doesn’t contain a 1 yet, remove the cells whose row or column already holds a 1. What’s left is the set of cells where 1 is still possible in that box.

This “digit-first” scan exposes constraints you’d never see cell by cell, because you’re reading whole rows and columns at once.

Step 2 — Only write notes that mean something

If a digit has one or two possible cells in a box, write it as a note in those cells. If it has three or more, write nothing yet and move on. This is NOTE-KU’s Two-Candidate Rule, and it’s what keeps your notes trustworthy: every note on the board says something precise, and you never have to clean up a box full of vague possibilities.

Work through every digit, 1 to 9. That is your first Notation Pass. Here is what it looks like on a real beginner puzzle — each small number is a digit noted in a box where it had only one or two possible cells:

Step 3 — Follow every consequence

Notes interact. When a digit is down to a single cell in a box, that position is settled, and the digit can be removed from every other note in that row, column and box. Removing it may settle another position somewhere else. Make it a habit: after every new note, look along its row and column for other notes of the same digit and ask what changed.

Step 4 — Iterate

Go back to the boxes you skipped. Eliminations often bring them down to one or two cells, so now they get notes too, which trigger new eliminations. Notation, elimination, notation, elimination. On an easy puzzle this takes one or two rounds; on an extreme one, seven or more. The method doesn’t change, only the number of passes.

Step 5 — When you run out of moves, test instead of guessing

On very hard boards you may reach a point where nothing moves. Pick a box where a digit has exactly two cells. Assume it’s in one of them, mark that assumption so it can’t be confused with your real notes, and follow the consequences. If they lead to a contradiction, the digit must be in the other cell — that’s a proof. In the NOTE-KU app this is Temp Mode.

Step 6 — Confirm everything in one sweep

When every empty cell holds exactly one candidate, stop and check once. Then fill in the answers digit by digit in one continuous pass. Nothing is decided here; it was all decided in the notation. That last sweep — the Final Pass — is the most satisfying moment in the method, and it only works because you never guessed along the way.

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