There are three rules. Fill the empty cells of a 9×9 grid with the digits 1 to 9 so that
- no digit appears twice in the same row
- no digit appears twice in the same column
- no digit appears twice inside the same 3×3 box, the blocks marked off by the heavy lines
Fill the grid without breaking any of the three and you are done. The digits that were there from the start cannot be changed.
Technique 1. The last free cell
If a row, a column or a box has only one empty cell left, the digit that belongs there is already decided: it is the one digit that unit is missing.
A fresh grid rarely has one of these. They appear once a few digits are down, and even a hard puzzle finishes its last cells this way.
Technique 2. The last remaining cell
This time you fix the digit first, not the cell. Pick an 8, then cross off every cell in the box where an 8 cannot go.
Technique 1 looks at a cell and hunts for its digit; technique 2 looks at a digit and hunts for its cell. A stuck grid usually opens from this side.
Technique 3. The last possible number
This time you fix on one cell and cross off every digit that already appears in its row, its column and its box. Cross off eight and the ninth is the answer.
The yellow cells are that cell's twenty peers, the cells sharing its row, column or box. A digit outside them cannot block this cell.
Notes
Block eight digits and the answer is settled, but most cells are not that blocked. Where several digits are still possible, write them into the cell — those are notes.
This is where the named techniques begin. Two cells carrying the same pair of digits is something you can only see once the notes are there.
Auto notes in settings recalculates the candidates every time you place a digit. Leave it off if you would rather keep them by hand.
What the words mean
| Term | Meaning |
|---|---|
| Row | A horizontal line. Nine cells |
| Column | A vertical line. Nine cells |
| Box | A 3×3 block marked off by the heavy lines. There are nine of them |
| Clue | A digit that was there from the start. It cannot be changed |
| Candidate | A digit that could still go in a cell. You jot these down as notes |
| Peers | The twenty cells sharing a row, column or box with a given cell |
Common questions
Do I need to be good at maths? No. In sudoku 1 to 9 are just nine symbols that differ from one another, so nothing is ever added or subtracted. Swap them for A to I and the puzzle works exactly the same.
Is there ever a cell you have to guess? No. Every puzzle here has exactly one solution: each time a digit is removed the puzzle is re-checked, and the removal is undone if a second answer appears. If you are stuck, there is something you have not spotted yet.
Are fewer clues always harder? Not reliably. The level depends on which technique the puzzle needs, which is why the level label here says something like “needs hidden singles”.
When you know the rules and it still won't come
People get stuck in much the same places. Four things account for nearly all of it.
- Guessing. One guess sends the grid quietly wrong, and the mistake usually surfaces ten cells later, by which point you cannot trace it back. If you are not sure, write it as a note instead.
- Skipping notes. Counting candidates in your head means re-scanning twenty cells every time you look at one, so you end up checking only two or three cells. Puzzles that fall to two or three cells are the easiest ones.
- Watching cells and never digits. Instead of asking “what goes in this cell?” over and over, pick one digit and hunt across the grid for where it can go. That is usually what breaks a stuck puzzle open.
- Forgetting the boxes. Rows and columns catch the eye; the 3×3 boxes are easy to miss even with lines around them. Scan the nine boxes on their own and something will turn up.
If you are doing all four and it still will not move, you have reached the point where a named technique is needed. The hint picks the easiest one that applies and points it out.
