Watch an experienced solver work through an easy puzzle and it looks like they are simply writing the answers down. They are not calculating faster than you — they are looking differently. Fast solving is mostly a repertoire of systematic eye movements that surface deductions in a reliable order, instead of wandering the grid hoping something jumps out. Those eye movements have names, they can be practiced deliberately, and this guide teaches the four that matter most.
Cross-hatching: the fundamental scan
Cross-hatching finds Hidden Singles in boxes, and it is the single most valuable habit in Sudoku. Pick a digit — say 7 — and a box that doesn't contain it yet. Every 7 already placed in a row passing through that box eliminates that entire row inside the box; every 7 in a crossing column eliminates that column. Mentally strike those lines through the box, along with any cells already filled. If exactly one cell survives, the 7 goes there.
The name comes from the hatching motion: you are sweeping rows and columns across the box like crosshatched pencil shading. Two details make it efficient:
- Work digit by digit, not box by box. Find every placed 7 on the grid first, then visit each box missing a 7. Keeping one digit in your head while your eyes move is far faster than re-loading a new digit for every cell.
- Start with the most frequent digits. A digit already placed six or seven times is heavily constrained — each remaining placement is usually forced, and each one you make constrains the rest. Count the digits at the start (many apps show this tally) and scan the crowded ones first.
Box counting: the fill-in scan
The complementary scan works cell-first rather than digit-first. Pick a nearly full unit — a box, row, or column with six or more digits placed — and ask which digits are missing, then whether any missing digit has only one legal cell, or any empty cell only one legal digit. Units with two or three empty cells resolve almost instantly, and every placement promotes other units toward the same threshold. This scan finds both Naked Singles and Hidden Singles without any pencil marks, and it is why strong solvers gravitate toward the crowded regions of the grid.
Follow the consequences
The most common inefficiency in novice solving is the restart: place a digit, then begin scanning the whole grid from scratch. Every placement changes exactly twenty cells' prospects — the eight others in its row, eight in its column, and four more in its box (its peers). The next deduction is overwhelmingly likely to be among them, or in the other boxes still missing the digit you just placed.
So adopt the rule: after every placement, check its peers before scanning anything else. Did the placement finish off a row to eight digits? Complete a cross-hatch in a neighboring box? Chains of four or five forced placements are the normal rhythm of easy and medium puzzles, and they only feel like chains if you follow them while they are hot.
Scanning for eliminations, not just placements
When singles dry up, the same disciplined eye movements find elimination patterns. During a digit scan, notice when a box's surviving cells for the digit all fall on one line — that is an Omission, and it needs no pencil marks at all, just the cross-hatch you were already doing. Notice when a digit is down to exactly two spots in a row, and whether another row mirrors it on the same columns — that is an X-Wing forming. Single-digit vision — the ability to see the grid as “the world according to the 7s” — is the entire perceptual foundation of the fish techniques.
A worked scanning routine
Putting it together, here is a complete routine for a paper or screen puzzle:
- Tally the digits. Note which digits are placed six or more times and which units are six or more full.
- Cross-hatch the frequent digits, most-placed first. Place every Hidden Single you find; after each placement, immediately re-check the boxes that digit touches.
- Sweep the crowded units with box counting to catch Naked Singles the digit scan missed.
- Repeat 2–3 until a full pass yields nothing. Only then add pencil marks and move up the technique ladder to subsets and fish.
The order embodies a principle worth stating plainly: exhaust cheap deductions before starting expensive ones. Every technique beyond singles costs bookkeeping, and every single you place makes the harder patterns simpler or unnecessary.
Training the scans deliberately
Because scanning is perceptual, it improves the way sight-reading music improves — through volume and repetition, not understanding. Understanding cross-hatching takes five minutes; making it automatic takes a few dozen puzzles. Two practice suggestions:
- Solve easy puzzles fast, on purpose. Easy puzzles are scanning practice. Timing yourself on puzzles below your level trains the eye movements under mild pressure and makes the habits stick.
- Drill one technique at a time. Scanning for a pattern you know is present is how recognition gets built. The technique picker generates puzzles that are guaranteed to require exactly the techniques you choose, so every puzzle is a rep of the pattern you are training — and the worked walkthroughs show each scan landing on a real board.
A last word of reassurance: speed is a by-product, not a goal. The point of scanning systematically is that you stop missing things, and the puzzle stops stalling. The stopwatch takes care of itself.