NOTE-KU, explained in full

The core idea

Most players solve sudoku by scanning for an obvious number, writing it in and scanning again. That works on easy puzzles. As difficulty rises, obvious placements disappear, notes get scribbled in a hurry, and the solver ends up with a board full of half-trusted information. Mistakes creep in and become impossible to trace.

NOTE-KU is built on a different idea: notes are the method, not a fallback. You use them systematically from the very first empty cell, you never write an answer until the notation has proven it, and you never guess. The solving happens in the notation. The final sweep only confirms it.

Two habits make this work. The first is digit-first thinking: instead of asking “what goes in this cell?”, you choose a digit and ask “where can it still go?” across the whole board. The second is restraint: you only write a note when it carries real information, which is what the Two-Candidate Rule enforces.

The language of the board

NOTE-KU thinks in boxes. The nine 3×3 boxes are named like a compass: TL TC TR across the top, ML MC MR through the middle and BL BC BR along the bottom. Inside any box, cells are numbered 1 to 9, left to right and top to bottom, like reading a page.

Box plus cell gives every square an address. TL-1 is the top-left corner of the grid, MC-5 the exact centre, BR-9 the bottom-right corner. Rows (1–9, top to bottom) and columns (1–9, left to right) matter because they carry constraints: a digit placed anywhere in a row rules it out of every other cell in that row, and the same goes for columns and boxes. Every technique in the method is a precise way of reading those three overlapping constraints.

Phase 1 — The Notation Pass

Select digit 1. Visit every box that does not already contain a 1. For each one:

1. List the empty cells in the box.
2. Remove every cell whose row already contains a 1 somewhere on the board.
3. Remove every cell whose column already contains a 1.
4. Count what is left and apply the rule below.

Then move to digit 2, then 3, all the way to 9 (to 6 in a Mini). Later digits benefit from earlier ones: the board grows more constrained with every digit you complete. After the first full pass you have your first constraint map — incomplete, but every note on it is meaningful.

Why skip boxes with three or more options? Because a note that says “this digit could be in any of four cells” proves nothing and has to be erased later, which is exactly how mistakes start. Waiting until a box is down to two cells means every note you write has constraining power. The Two-Candidate Rule in depth.

Phase 2 — Elimination & Iteration

Every new note changes what is possible elsewhere. After each one, look at the other notes for the same digit in the same row and column and ask: does this tell me something I didn’t know? When a box is left with a single possible cell for a digit, that position is settled; project it across its row, column and box and remove that digit from every note it touches.

Sometimes one note triggers a chain: note A fixes where note B goes, which fixes note C, which eliminates note D. These chains are the engine of the method, and they are why NOTE-KU asks you to pause briefly after every note rather than racing ahead.

Then iterate. Return to the boxes you skipped. Eliminations may have brought some of them down to one or two cells; note those, follow their consequences, and repeat — notation, elimination, notation, elimination — until every empty cell on the board holds exactly one candidate.

A digit is exhausted for this pass when every box either already holds it, has one or two notes for it, or still has three or more open cells and was deliberately skipped. Nothing more can be done with that digit right now, so move on. In the app, a small ✓ NOTED badge on the digit bar tells you when you’ve reached that point.

On harder boards, the basic cascade eventually runs dry. The books introduce named patterns for those moments — the Locked Pair, the Locked Triad, the Arrow and the Grid Read — which apply the same digit-first logic to wider constraint patterns. They extend the method; they never replace it.

Phase 3 — The Final Pass

When every empty cell holds exactly one candidate, you have reached the threshold. The puzzle is solved; what remains is confirmation. Verify once that no cell holds two candidates and no box was missed, then begin the sweep.

Start with the last digit whose note completed the board and fill in all of its confirmed positions. Move to the next digit in ascending order and continue until the board is full. One continuous sweep: no analysis, no decisions, every number going exactly where the notation said it would.

Resist the urge to fill in single candidates early. Writing answers mid-notation breaks the rhythm and invites mistakes; the patience of Phase 2 is what makes Phase 3 inevitable. In the app, Undo is locked during the Final Pass for the same reason: by then, nothing should need undoing.

Temp Mode — proof by contradiction

On the hardest puzzles you can reach a point where no box has a digit down to one or two new cells and no elimination is available. NOTE-KU never guesses. Instead it tests:

1. Find a box where a digit has exactly two candidate cells.
2. Assume it goes in one of them and mark that assumption as a temporary note, in a colour that can’t be confused with your permanent notes.
3. Follow the consequences. If they lead to a contradiction — a digit with nowhere left to go, or two of the same digit in a row, column or box — the assumption was false.
4. The digit is therefore in the other cell. That is a proof, not a guess. Clear the temporary notes and continue with what you’ve proven.

If the consequences run out without a contradiction, the test has proven nothing yet: clear it and test the other candidate, or a different pair. A full walkthrough of Temp Mode.

Why it scales with difficulty

The most common question about NOTE-KU is whether it really works on expert puzzles. It does, with the same method applied more deeply.

In every case: same phases, same rule, same Final Pass.

What NOTE-KU is not

• Not “full candidate mode”. You do not write every possible digit into every cell. You note a digit only when it is down to one or two cells in a box.
• Not guessing. Temp Mode tests an assumption and keeps only what a contradiction proves.
• Not a list of tricks to memorise. Digit-first notation, elimination and iteration solve the large majority of puzzles on their own.
• Not a race. You can play against the clock, but the method rewards patience first.