How to Solve Sudoku, from Basics to Advanced Techniques

Sudoku is a logic puzzle played on an eighty-one-cell grid, nine rows of nine, filled with the numbers 1 through 9. The name has numbers in it, but you never add or multiply anything; the only rule is that the same number cannot appear twice in a group, so the puzzle works exactly as well with nine colors or symbols in place of digits.

Its root is the Latin square, which arranges the same symbols once per row and once per column. The modern form, with the added 3x3 box constraint, is first known to have appeared in a 1979 American puzzle magazine under the name Number Place. It picked up the name Sudoku in Japan in the 1980s and spread worldwide after a British newspaper began running it in 2004.

The shape of the board

The board is nine cells wide and nine tall, eighty-one cells total. A horizontal line of nine is a row, a vertical line is a column, and a bold-bordered block of nine cells is a box. There are also nine boxes, so every cell belongs to exactly one row, one column, and one box at the same time. Those three groups are the entire set of constraints on that cell.

How to place a number

Each row needs 1 through 9 once each, each column needs the same, and so does each of the nine boxes. Put another way: to place a 5 in a cell, that 5 must not already appear anywhere in the cell's row, column, or box. In practice, solving is less about finding where a number goes and more about eliminating where it cannot go.

When you're done

The numbers printed from the start are called givens, and they cannot be changed. Once every remaining cell is filled and the result satisfies all three rules above, the puzzle is finished. There is no time limit and no required order; you can fill any cell first.

From here on, this section covers what this specific app does. Sudoku apps differ in these details, so reading this once should save you some confusion.

One puzzle a day, the same for everyone

The puzzle is generated from that day's date. Anyone who visits on the same day gets the same puzzle, and a new one opens when the date changes. Generating and solving both happen entirely in your browser, so nothing is exchanged with a server and no account is needed.

Only puzzles with exactly one solution

The generation order is a little unusual. We first build a complete, valid grid, then clear cells one at a time. After each cell is cleared we count how many solutions the puzzle has, and if that count reaches two or more, we put the cell back. So the puzzle you see always has exactly one solution; there is never a point where guessing is structurally required.

Cells are cleared in pairs, chosen symmetrically across the center of the board, and clearing stops once the number of givens drops to around thirty-six. That pairing is why the board tends to look balanced left to right and top to bottom.

What the red highlight catches

The numbers printed from the start show up bold and black and cannot be changed by tapping them. Numbers you enter show up in blue, and if the same number appears twice in a shared row, column, or box, those cells turn red.

One distinction worth keeping in mind: the red highlight only checks for duplicates. It is not checked against the actual solution, so a wrong number that has not yet collided with anything still shows in plain blue. Having no red cells doesn't mean everything is correct, so if the board is full but the solved message has not appeared, there's a wrong number hiding somewhere.

Entering and erasing

Tap an empty cell to select it, then tap a number button below or press 1 through 9 on your keyboard to place it. To erase, tap the erase button or press 0, Backspace, or Delete. Nothing happens if you press anything while a given cell is selected.

We also want to be clear about what this app does not do. There is no hint button that reveals the answer, no pencil marks for jotting candidate numbers in a cell, and no timer or mistake counter. There is no undo either, but any number you enter can always be erased and re-entered, so a single mistake does not ruin the puzzle.

Saved progress and finishing

Filled cells are saved in this browser, so they survive a refresh or closing and reopening the tab. When the date changes, yesterday's save is discarded and a new puzzle opens; if a saved grid's givens do not match today's puzzle, it is treated as a different puzzle and not loaded.

The moment all eighty-one cells match the solution, the solved message and a share button appear. The share text carries only the date and whether you finished, plus how many cells were filled if you share before finishing. It never includes what you entered in which cell, so sending it to someone still mid-puzzle will not leak the answer.

These are things you work out by eye and by reasoning; the app won't find them for you. Once learned, though, they carry over to any Sudoku puzzle, not just this one.

Start with scanning

Pick one number and chase only that one. Say you pick 5: scan the board for rows and columns that already contain a 5, and see which cell in each box is still open for it. If only one open cell remains in a box, that cell is settled. Cycling through 1 to 9 this way usually turns up several cells early on.

Finish nearly full lines first

If a row, column, or box already has eight of nine cells filled, the last cell is settled just by counting what's missing. Filling these easy spots first often opens a chain of new certainties in the lines that number touches, so clearing the easy spots before tackling the hard ones tends to be faster overall.

One candidate left means it's settled

Pick an empty cell and cross off every number already present in its row, column, and box. If only one number survives, that is the answer. Where scanning works number by number, this works cell by cell, so the two methods tend to catch different cells. If one stalls, switch to the other.

Past the midpoint, the three techniques above stop producing new cells for a while. These are the techniques for that stretch. This app has no pencil-mark space, so you'll need to hold candidates in your head or jot them on paper.

Hidden single

A cell can be settled even while several candidates remain in it. If a given number can only go in one cell within a row, column, or box, that number is the answer for that cell no matter how many other candidates it still lists, because if that cell held anything else instead, this number would have no other cell left in the group to go to. This is the spot beginners miss most often.

Candidate pairs

If two cells in the same group each have exactly the same two candidates left, say both are down to 3 and 7, then 3 and 7 will end up split between exactly those two cells. So every other cell in that group can drop 3 and 7 from its own candidates. That elimination is often what opens the next settled cell. The same logic extends to three cells splitting three numbers.

Box and line intersection

If, within one box, every possible cell for a given number falls in the same row, that number must end up in that row's portion of the box. That means the same number can be eliminated from that row in the other two boxes. It works the other way too: if a number's only possible cells in a row all fall within one box, eliminate that number from the rest of that box. Learning to watch boxes and lines together noticeably shortens the mid-puzzle stall.

The board is full but not marked solved

As noted above, the red highlight only catches duplicates. If every cell is filled but the solved message never appears, a wrong number is hiding somewhere without ever colliding with anything. The fastest fix is usually to erase your least-confident blue entries first and re-check those spots; a wrong cell tends to drag its whole line wrong with it, so clearing and rebuilding one suspicious box at a time also works well.

Stuck on one cell for too long

With around thirty-six givens, the midgame naturally has many cells with several candidates left. Staring at one cell longer does not shrink its candidate list, so if you're stuck, move on, switch numbers, and take another full pass of scanning. Opening one cell elsewhere usually resolves the one you were stuck on too.

Watching boxes but missing lines

Because the 3x3 boxes are visually obvious, it's easy to scan by box alone. Rows and columns cut across boxes differently, though, so a certainty invisible inside a box often shows up plainly in a row. After a pass through the boxes, do a pass through the rows, then a pass through the columns, rotating your reference on purpose.

The urge to guess

This puzzle has exactly one solution, so there is never a point where guessing is required to move forward. If you're stuck, there's a piece of logic you haven't spotted yet, not a coin flip where luck decides. There is also no undo, so a single guess can be hard to trace back from later. It's better to fill in only the cells you're sure of and take a break than to guess.