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How to Solve Sudoku: A Beginner's Guide
Sudoku looks like a maths puzzle, but you never actually add anything up. It is a puzzle of pure logic: every answer is already decided by the numbers on the board, and your only job is to uncover them in the right order. Once you learn a handful of techniques, the grid stops feeling like a wall of empty squares and starts feeling like a conversation. This guide walks you through that, from the single rule that governs everything to the four techniques that solve almost every beginner and intermediate puzzle.
The one rule behind every Sudoku
A standard Sudoku is a 9×9 grid split into nine 3×3 boxes. Some squares are filled in to start; the rest are blank. There is exactly one rule, and the whole game flows from it:
Every row, every column, and every 3×3 box must contain the numbers 1 to 9, with no repeats.
That is the entire game. There is no arithmetic and no guessing required in a well-made puzzle - a proper Sudoku always has exactly one solution that you can reach through logic alone. If you find yourself flipping a coin, stop: there is almost always a square somewhere on the board whose answer is already forced, and the techniques below are simply ways of finding it.
Brand new to it? Start smaller. A 4×4 grid (numbers 1 to 4 in four 2×2 boxes) uses the exact same rule and teaches the same instincts in a fraction of the time. Mochi Sudoku opens on gentle 4×4 and 6×6 boards before it ever hands you a full 9×9, so the leap never feels steep.
Technique 1: Scanning (cross-hatching)
Scanning is the first thing every solver does, and it cracks more of the early grid than anything else. Pick a number - say, 5 - and look at where the 5s already sit. Because no row, column, or box may hold two 5s, each existing 5 "blocks" its whole row and its whole column for that number.
Now choose one 3×3 box that still needs a 5. Trace the rows and columns running through it. If a 5 elsewhere on the board rules out every empty square in that box except one, that survivor must be the 5. You have placed a number without considering anything but exclusions. Work through 1 to 9 this way, box by box, and a surprising amount of the puzzle fills itself in.
Technique 2: The last empty square
This one is almost too simple, but it is easy to miss when you are staring at the whole board. Any time a row, column, or box has only one blank square left, the answer is whatever number is missing from that group. Eight of the nine numbers are present, so the ninth is forced.
Get into the habit of glancing at near-complete rows, columns, and boxes after every few placements. Each number you write makes its neighbours more complete, so a board that felt stuck five moves ago often has two or three "last squares" waiting once you look again.
Technique 3: Pencil marks (candidates)
When scanning stops handing you easy wins, switch from filling answers to noting candidates - the small list of numbers that could still legally go in each empty square. In a paper puzzle you pencil these tiny numbers into the corners; in a digital game you toggle them on.
Candidates turn a vague board into a precise one. Once you can see, for example, that a square can only be a 2 or a 7, the next two techniques become easy to spot. The discipline is to keep them honest: every time you place a real number, erase that number from the candidates in its row, column, and box. Out-of-date pencil marks are the single biggest cause of mistakes.
Good to know: a clean digital game does the bookkeeping for you. Mochi Sudoku has a notes mode that places candidates with a tap and clears them automatically as you solve, so you can focus on the reasoning instead of the erasing.
Technique 4: Hidden singles
A "naked single" is a square with only one candidate left - place it and move on. A hidden single is sneakier and far more satisfying. It is a square that has several candidates, but one of those candidates appears nowhere else in the row, column, or box.
Suppose a 3×3 box still needs a 4, and within that box only one empty square even lists 4 as a candidate. It does not matter that the square also lists 1 and 8 - if 4 has to go somewhere in this box and there is only one place it can legally land, that square is a 4. Hunting for hidden singles, one number at a time across each box, row, and column, is how you break through the middle of a tougher puzzle.
Technique 5: Naked pairs
Here is your first taste of "advanced" Sudoku, and it is gentler than it sounds. If two squares in the same row, column, or box share the exact same two candidates - say both can only be {2, 6} - then 2 and 6 are locked into those two squares, even though you do not yet know which goes where.
The payoff is elimination: because 2 and 6 must use up those two squares, you can safely remove 2 and 6 from every other square in that shared group. Often that removal creates a fresh naked single or hidden single nearby, and the chain reaction carries you forward. Naked pairs are the bridge from "easy" to "medium" puzzles.
A simple solving routine
Put it together and you have a reliable loop that solves the vast majority of puzzles:
- Scan each number 1 to 9 and place every obvious cross-hatch and last-square answer.
- When scanning dries up, fill in candidates for the remaining empty squares.
- Sweep for naked singles (one candidate) and hidden singles (a number with one home).
- Use naked pairs to eliminate candidates and reopen the board.
- Every time you place a number, update the candidates around it, then loop back to step 3.
Notice that guessing never appears in the list. If you ever feel forced to guess, it almost always means a candidate somewhere is stale - back up, re-check your pencil marks, and the forced move usually reappears.
Common beginner mistakes
- Forgetting to update candidates. Place a number, then immediately clear it from its row, column, and box. Stale marks lead you to "impossible" contradictions that are really just bookkeeping errors.
- Tunnel vision on one box. If a region stalls, move on. A placement on the far side of the board often unlocks the square you were stuck on.
- Guessing to save time. A single wrong guess can quietly poison ten later squares. Slower logic is faster than untangling a contradiction.
- Skipping the easy scan. Even on hard puzzles, always start with plain scanning - it clears the clutter so the clever techniques have less to chew through.
Where to go next
The fastest way to internalise all of this is simply to play. Start on the smaller grids until scanning and last-squares feel automatic, then step up to 9×9 and let the candidate techniques carry you. Within a few puzzles you will stop reading the board square by square and start seeing whole numbers click into place. If you enjoy the deductive feel of Sudoku, you will likely love the other pure-logic puzzles below, which lean on the same "what is already forced?" instinct.