Scanning

Scan the Board Systematically

Random scanning is the quiet reason most beginners stall. A fixed route through the grid finds more numbers with less effort — and never leaves an easy placement sitting unseen.

Why a routine beats a hunch

Left to instinct, the eye drifts to wherever the board looks busiest and skips the rest. You place a number, jump somewhere new, and forget which units you have already checked. Ten minutes later you are convinced the puzzle is hard when really you have just never looked at the bottom-left box. A routine removes that waste: it guarantees every unit gets attention and turns solving from a nervous hunt into a calm, repeatable pass.

One number at a time

The most reliable route is by digit. Pick 1 and ask, in each of the nine boxes, whether the 1 already has a home; where it does not, cross off the rows and columns that carry a 1 elsewhere and see if a single empty cell remains. Then do 2, then 3, all the way to 9. Because every placement closes lines for the digits that follow, a single top-to-bottom pass of all nine numbers usually cracks far more of the grid than an hour of jumping around.

Then sweep by unit

When the by-digit pass slows down, switch axes and go by unit instead. Take each box, row and column in turn and ask which numbers it is still missing, then check whether any of those numbers has only one legal cell left inside it. The two routes catch different things — the digit sweep is best for hidden singles, the unit sweep for naked ones — so alternating between them keeps placements coming after either one alone would have dried up. A useful signal marks the handover: when a complete pass of all nine digits adds nothing, the digit route is spent for the moment, and the unit route will nearly always turn up the placement it missed. Treat that stall not as a dead end but as a cue to change axis, and the board keeps giving long after a single method would have left you staring at it.

Mark where you stopped

The point of a system is that you can pause and resume without losing your place. If you keep your pencil notes current, the board itself remembers your progress: a fully noted grid shows exactly which cells are still open and what they can hold, so you never have to redo a sweep you already finished. That is the real economy of scanning in order — no unit is ever checked twice by accident, and none is ever missed.

A worked pass

Suppose you start your digit sweep on the 6s. The top band of three boxes already holds two 6s, so in the third box the 6 is squeezed into a single row; combined with a 6 sitting in one of that row's columns elsewhere, exactly one cell survives and the 6 drops in. That placement now closes a new column, which on your next digit — the 7 — leaves the middle box with only one home for its 7. One orderly pass, and two placements that random scanning might never have connected have fallen out in sequence.

Make it automatic

Do this on enough boards and the route stops feeling like a checklist and becomes the way you see. Fast solvers are rarely thinking harder than you; they are simply following a fixed path so relentlessly that placements appear to fall out on their own. Build the habit on a gentle grid at Easy Sudoku, carry it into Medium Sudoku where it does the most work, and put it to the test on today's Daily Sudoku.