How to solve Sudoku faster

1 September 2026 · 7 min read

Fast solvers are not thinking faster. They are looking in better places, in a fixed order, and not re-checking things they have already ruled out. Almost all of the improvement available to an average solver is in search order rather than reasoning speed.

Where the time actually goes

Time a solve honestly and the breakdown is usually something like this: a small slice spent placing digits, a larger slice spent searching for the next move, and a large slice spent re-searching regions you already looked at because you had no system and lost your place.

That third slice is the one to attack. It needs no new technique — only a routine you follow the same way every time.

A scanning routine

Do these in order. Move to the next step only when the current one produces nothing, and go back to step 1 after every placement.

1. Cross off the digit you just placed. A new digit changes 20 cells. The next move is very often adjacent to the last one, so this is the cheapest check on the board.
2. Count the digits, work the most common one. Whichever digit is already placed the most times is the most constrained. Take it through the boxes that are missing it.
3. Work the fullest units. A box with seven digits is worth ten times a box with two. Rank by how full they are, not left to right.
4. Sweep every digit through every box. Nine digits, nine boxes, in order, without skipping. Boring and reliable — this is where hidden singles are found.
5. Check the box/line intersections. Pointing pairs and box/line reduction are the best-value techniques in the game because they need no pencil marks — just “where can this digit go in this box?”
6. Only now start marking. And mark one unit at a time, scanning it as you go.

Steps 2 and 3 are where most of the speed is. Beginners scan the grid in reading order, which means spending equal effort on the emptiest and fullest parts of the board. The fullest parts are where the forced moves are.

Boxes before lines

When you have a choice, look at a box. Three-by-three fits in one fixation; a row spans the whole grid and your eye has to travel and remember. Same information, much less effort.

This is not just ergonomics — it is why this app’s Explain next step checks boxes first, then rows, then columns. The explanation you get names the unit you were most likely to have been looking at anyway, which makes it teach rather than merely inform.

Do not mark up front

Filling in every candidate before starting feels productive and usually costs more than it saves. It takes several minutes, needs constant upkeep as you place digits, and on anything below Hard the puzzle will be over before it repays the investment.

The trigger to start is behavioural: the first time you go all the way round the grid and place nothing. That is the point where you have exhausted what you can hold in your head. Before it, marking is procrastination; after it, scanning is. How much to mark, and how to keep it honest.

The eliminate-then-sweep loop

This is the single most useful habit for hard puzzles, and it is easy to state: after every elimination, immediately re-sweep for singles.

Techniques like pairs, triples and X-wings never place a digit. All they do is remove candidates — and the only reason removing candidates is useful is that it can create a single. Finding a naked pair and then continuing to hunt for more pairs is a common and expensive mistake: the pair you just found has probably already handed you the next placement.

Solving a hard Sudoku is that loop, over and over: eliminate, sweep, eliminate, sweep.

What wastes the most time

• Rechecking cells you already ruled out. The fix is order: if you always sweep digits 1 through 9 through boxes 1 through 9, you know where you have been.
• Hunting advanced patterns too early. An X-wing takes real effort to find, and virtually every position containing one also contains something cheaper. Sweep first.
• Guessing. The cost is not the wrong digit, it is that every deduction afterwards is now suspect. When you hit a contradiction twenty moves later you cannot tell whether the guess was wrong or your reasoning was, and the honest response is to unwind all twenty.
• Working with stale pencil marks. A mark you did not clear after placing a digit will eventually be acted on, and everything built on it is wrong. This is the most common way a solve fails.
• Restarting instead of finding the mistake. If the grid has gone wrong, the contradiction tells you which unit is broken. Rebuilding that unit’s candidates from the placed digits is far quicker than starting over — and it is how you learn not to repeat it.

How to actually practise

Volume alone plateaus quickly. Two things move the needle:

• Stay one level below frustration. Difficulty here is defined by the hardest technique required, so a level you finish comfortably means you have that technique. Move up when its hardest step comes fast, not when you can grind through. What difficulty labels actually mean.
• Name the move that unstuck you. This is the whole difference between practice and repetition. “Hidden single in a column” is a pattern you will find faster next time; “I finally spotted it” is not. When you cannot name it, ask — Explain next step exists to answer exactly that, and it names the technique rather than just filling the cell.

And do not chase the clock. Timing yourself measures whether you are having a good day. Reviewing which technique you were slow to spot tells you what to work on.

Every diagram on this page is a real position from a generated puzzle, and every elimination shown is checked against that puzzle’s unique solution as part of the test suite. Want a move explained on your own board? Play a puzzle.