The first time most people open a Sudoku, they fill in two or three obvious numbers, feel briefly clever, and then hit a wall. The grid stops giving anything up. You stare at it, nothing moves, and the quiet assumption sets in that you are missing some math gene other people have.
You are not. Sudoku is not a math puzzle. There is no arithmetic anywhere in it, and the digits 1 to 9 could just as easily be nine different colors or nine animals. It is a logic puzzle wearing numbers as a costume. We have taught a fair number of nervous beginners to solve these, and the gap between “stuck on every puzzle” and “finishing easy and medium boards” is usually three or four small techniques, learned in the right order. This guide is those techniques. You can play a free board alongside it if you want to try each one as you read.
The one rule everything comes from
A standard Sudoku is a 9x9 grid, split into nine 3x3 boxes. Some cells start filled. Your job is to fill the rest so that every row, every column, and every 3x3 box contains each of the numbers 1 through 9 exactly once.
That is the whole rule. No number repeats inside any row, any column, or any box. Everything below is just a different way of asking the same question: given what is already placed, where is a number forced to go?
One honest thing to settle up front. A properly made Sudoku has exactly one solution, and you can always reach it by logic alone. You never have to guess. If you find yourself wanting to “try a 4 and see what happens,” that is a sign you have missed a deduction, not a sign the puzzle needs luck. We will come back to why guessing is a trap.
Technique 1: scanning, the workhorse
Scanning, also called cross-hatching, is the technique you will use more than all the others combined. It is how you place most numbers on an easy board.
Here is the move. Pick a single digit, say 7. Find a 3x3 box that does not have a 7 yet. Now look at the rows and columns that pass through that box. Wherever a 7 already exists in one of those rows or columns, it “blocks” the cells in line with it. You are mentally drawing lines out from every existing 7 and crossing off the cells they hit.
Often this leaves two or three open cells in the box, which is not yet an answer. But sometimes it leaves exactly one. When only one cell in the box can possibly hold the 7, that is where the 7 goes. This is called a hidden single: the number is hidden in a crowd of empty cells, and scanning is how you find it.
Work one digit through the whole grid, box by box, then move to the next digit. Hidden singles are the most common thing on easy and medium puzzles, and plenty of beginner boards fall to scanning alone.
Technique 2: the last empty cell
This one is almost too simple to call a technique, but it is worth naming because it keeps your momentum going.
Whenever a row, a column, or a box has just one empty cell left, you are done thinking. The eight filled cells already use eight of the nine digits, so the missing one is whatever number is not there yet. Count 1 through 9 against what you see, find the gap, fill it.
Every number you place creates new “almost full” lines elsewhere, so get in the habit of glancing around after each placement. A single 7 dropped into the grid can be the eighth number in a row you had been ignoring, and now that row solves itself.
Technique 3: naked singles
Scanning works from the number’s point of view: you pick a digit and hunt for its one legal home. A naked single works from the cell’s point of view, and it is the other half of beginner solving.
Pick an empty cell. List the digits already sitting in its row, its column, and its box. Cross all of those off the numbers 1 through 9. Whatever survives is what could legally go in that cell. If only one number survives, the cell has a naked single, and you place it.
Naked singles are rare at the very start of a puzzle, when most cells still have many options, and they become common near the end, when the grid is crowded. The fastest way to catch them is to stay reactive. Every time you place a number, look at the empty cells sharing its row, column, and box, and ask whether you just knocked one of them down to a single option.
Technique 4: pencil marks, for when scanning dries up
On easy boards you can hold everything in your head. On a medium board you will reach a point where scanning stops producing and naked singles are not jumping out either. This is where pencil marks earn their keep, and the good news is that the Sudoku game on Mindplay has a notes mode so you are not actually erasing graphite.
A pencil mark is just a small note in the corner of a cell listing every number that could still legally go there. You build them the same way you find a naked single: for each empty cell, write the digits not blocked by its row, column, or box.
Once a cell is down to a single pencil mark, that is a naked single you place. The real payoff is that pencil marks make patterns visible that you cannot hold in your head. The most useful beginner pattern: if two cells in the same row, column, or box both show the exact same two candidates, say 3 and 7, then those two numbers are claimed by those two cells. You can safely erase 3 and 7 from the other cells in that line, which often uncovers a fresh single somewhere else. This is called a naked pair, and it is the first technique that feels like real deduction rather than counting.
Pencil marks take a little patience to maintain, and that is the honest cost. But they are what carries you from “I can do the easy ones” to “I can finish a medium without giving up.”
Why guessing is a trap
When a board goes quiet, the tempting move is to pick a fifty-fifty cell, guess, and push forward. Resist it. Because a valid Sudoku has exactly one solution reachable by logic, a guess does not unlock anything you could not have deduced. What it does is poison the grid: if your guess was wrong, you will keep placing “correct” numbers on top of a broken board, and the contradiction can surface ten moves later, far from the mistake. Now you cannot tell which placements were real and which followed from the bad guess.
Slower and certain beats fast and wrong here. If you are stuck, you have missed a deduction, not run out of logic. Re-scan each digit, refresh your pencil marks on the busiest box, and look again. The next number is always in there.
Where to start
Begin on easy boards and use only scanning and the last-empty-cell trick until they feel automatic. When easy puzzles stop being interesting, move to medium and bring in naked singles, then pencil marks when you stall. Do not jump to hard boards to prove something. Hard puzzles need techniques beyond these four, and grinding one for an hour teaches less than finishing three mediums cleanly.
The fastest way to internalize all of this is reps, not reading. Open an easy Sudoku, find one hidden single by scanning, and place it. That single number is the whole game in miniature. Everything else is just doing it again until the grid is full.
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Frequently asked questions
Do you need to be good at math to solve Sudoku?
No. Sudoku is pure logic. You place the digits 1 to 9 so each row, column, and 3x3 box contains each one once, and there is no arithmetic involved.
Should beginners ever guess?
No. Every valid Sudoku has one solution reachable by logic. Guessing tends to create errors that surface much later, so when stuck, look harder rather than guess.
What technique should I learn first?
Scanning. Checking where a given digit can and cannot go across each box, row, and column is the workhorse that solves most easy and medium puzzles.
What are pencil marks?
Pencil marks are small candidate numbers you note inside a cell to track its possible digits without committing, which becomes essential once simple scanning dries up.