How to Solve Sudoku: A Beginner’s Guide

The grid and the words for its parts

A sudoku is a 9 × 9 grid of 81 cells, divided into nine 3 × 3 boxes. A cell belongs to one row, one column and one box, and together those 20 other cells are the cell's "house mates": no digit may repeat among them. The givens are the digits printed at the start. The puzzle is finished when every cell holds a digit and no row, column or box repeats one.

Technique 1: scanning for where a digit must go

The first and most productive technique is to pick a digit and ask, box by box, where it can go. Take the digit 5. Look at a box that does not yet contain a 5. Every row and column that already has a 5 elsewhere crosses out some of the box's cells; if only one cell is left, the 5 goes there. Solvers call this cross-hatching, and the result is a hidden single: the digit has only one home in the box.

Do this for every digit from 1 to 9, then start again, because each digit you place creates new eliminations. On an easy puzzle, scanning alone finishes most of the grid.

Technique 2: what can this cell be?

The opposite question is just as useful. Pick an empty cell and list the digits already in its row, column and box. If eight of the nine digits are taken, the cell is the ninth: a naked single. Cells in crowded rows and boxes are the place to look. Many solvers alternate the two questions: "where does this digit go?" and "what does this cell hold?".

Pencil marks: when to start writing small

When neither question produces a certain answer, it is time for pencil marks: small notes of every digit a cell could still hold. The Daily Sudoku has a Pencil mode for this. Do not mark every cell at once; mark the cells with the fewest options (two or three candidates), since those are the ones that will resolve first. A full set of candidates is only worth the time on hard puzzles.

Keep the marks honest: whenever you place a digit, remove it from the pencil marks of its row, column and box. A stale pencil mark is the most common cause of a "sudoku with no solution".

Technique 3: pairs and triples

With pencil marks in place you can see two patterns that eliminate candidates without placing anything:

• A naked pair: two cells in the same house that both contain exactly the same two candidates, say 3 and 8. Those two cells must hold the 3 and the 8 between them, so 3 and 8 can be removed from every other cell in that house.
• A hidden pair: two digits that appear as candidates in only two cells of a house. Those cells must hold those two digits, so any other candidates in them can be erased.

Triples work the same way with three cells and three digits (the three cells need not each hold all three digits). Pairs are the first technique that feels like "real" sudoku solving, and medium puzzles usually need one or two.

Technique 4: pointing and claiming

Look at a box and a digit that can only go in two or three cells of that box. If those cells all sit in one row, the digit is in that row inside this box, so it cannot be anywhere else in that row outside the box. This is a pointing pair (or triple). The reverse, where a digit's only places in a row all fall inside one box, lets you remove it from the rest of that box: claiming (also called box-line reduction). Both are quick to spot once you look for lines of candidates inside a box.

A method for a whole puzzle

1. Scan every digit with cross-hatching. Place every hidden single you find and repeat until nothing new appears.
2. Check crowded cells for naked singles.
3. Pencil-mark the cells with two or three candidates only.
4. Look for naked and hidden pairs in rows, columns and boxes; remove candidates; return to step 1.
5. Look for pointing pairs and claiming; return to step 1.
6. If the grid is still stuck, the puzzle needs the techniques in the advanced guide, starting with X-wings.

Never guess. If you are tempted, you have missed an elimination; go back to step 1 with fresh eyes. On the Daily Sudoku, clashing digits are flagged, which catches a slip early, but a wrong digit that does not clash yet will poison the grid several moves later.

Easy, medium and hard days

The daily difficulty is about which techniques the puzzle needs, not how many givens it has. Easy days fall to singles; medium days need pairs and pointing; hard days need at least one advanced technique. The clock ranks the leaderboard by time, so on easy days the skill is fast, accurate scanning; on hard days it is knowing which pattern to look for.

Common mistakes

• Filling a digit because it "fits". Fitting is not enough; it must be the only option. Check the row, column and box every time.
• Pencil-marking everything. It takes minutes and hides the useful marks among the noise.
• Forgetting to update pencil marks. Every placement should clear that digit from its three houses.
• Scanning only rows. Columns and boxes give different eliminations; rotate through all three.
• Getting stuck on one region. If a box will not move, scan the rest of the grid; a digit placed far away often unlocks it.

Glossary

• House: a row, column or box; the three groups in which digits cannot repeat.
• Given: a digit printed at the start.
• Candidate: a digit a cell could still hold.
• Naked single: a cell with one candidate left.
• Hidden single: a digit with one possible cell left in a house.
• Naked pair: two cells in a house with the same two candidates.
• Hidden pair: two digits confined to the same two cells of a house.
• Pointing pair: a digit confined to one row or column within a box.