How to play Sudoku without guessing

Sudoku asks you to fill each row, column and box with the digits one through nine, without repeats. Start with missing digits and use the crossing constraints to justify every placement; arithmetic and the size of the printed numbers do not matter.

Read the board as overlapping sets

A row is a horizontal line, a column is a vertical line, and a box is a smaller square bounded by the heavier lines. A cell belongs to all of them at once. A digit that fits the row may still be forbidden by its column. Printed givens are fixed information; your entries must work around them.

Imagine a row missing only four and seven. Its left empty cell sits in a column that already contains seven. That cell must be four, so the other empty cell becomes seven. This is a local example, not a complete puzzle: it demonstrates why checking a row alone is insufficient.

A starting routine

Scan nearly complete rows, columns and boxes. Write down their missing digits.
For an empty cell, remove anything already present in its row, column or box.
Place a digit only if it is the last remaining candidate, or if it has only one possible home in a unit.
Recheck the units touched by your new digit. They may now contain another forced move.

Do not repeatedly sweep every cell with equal attention. A newly completed row changes the candidate picture nearby, so follow that information first.

A small worked comparison

Observation	What you know	What you cannot conclude
A row lacks four and seven	Both must appear in that row	Which empty cell gets which
One empty cell sees a seven in its column	Seven cannot go there	Anything about unrelated rows
Only four remains for that cell	Place four	That every two-candidate cell is solved

The last distinction matters: having a short candidate list is useful, but two possibilities are still two possibilities.

When the easy scan stops

Use pencil marks to preserve the legal candidates. Then inspect one digit across a box: existing copies in crossing rows and columns may rule out every position except one. This is often easier to see than testing every cell separately.

If you cannot explain a proposed entry without saying “it looks right,” leave it as a note. A completed-looking grid with a guessed error can hide the original mistake far from the current focus. Correctness comes from the reason for a move, not from how long the board appears to have no visible conflicts.

Solve a nearly complete row

Here is a row with two gaps. The letters label cells, not possible digits; a dot means a square still needs a number.

Cell	A	B	C	D	E	F	G	H	I
Entry	one	two	three	.	five	six	.	eight	nine

The missing set is four and seven. Suppose the column through D already contains seven, while the column through G contains four. Those crossing clues settle the row without any tentative entries.

D cannot be seven because its column already has seven, so enter four at D.
G now takes seven, the row's only remaining digit.
Check the boxes containing D and G: the new entries remove four and seven respectively from their other empty cells.

If neither crossing column excludes anything, the row remains unresolved. Write four and seven as notes in both gaps and move to a different area. An unfinished pair is a useful record of what you know; it is not permission to pick an arrangement.

Read a completed box correctly

A box with eight entries is missing one digit, but you must still check the crossing row and column before entering it. If the missing digit is already present in either crossing unit, an earlier entry is wrong. A full set in one box does not excuse a repeat elsewhere.

For a final board check, inspect the rows, then the columns, then the boxes. Each must contain every digit exactly once. A board can have perfectly ordered-looking rows and still repeat a digit down a column. The three overlapping requirements apply throughout the game, including the final move.

A small exercise

Change the example so D's column contains four instead of seven. Now D must be seven and G must be four, provided their boxes permit those entries. The row's missing set stayed the same; a crossing constraint changed the answer. This is the central habit to learn before studying named patterns: use the information that reaches the square from every direction.

Where to play

Ninefold gives you five independent difficulty tracks for practicing the basic rules. Begin on Easy and use pencil notes to keep possible digits separate from placements.