Pass one: scan missing digits

Start with the most complete rows, columns, and boxes. For each unit, list its missing digits and test the available cells. Crosshatching between boxes and lines is especially effective early in a puzzle. Place only digits whose positions are forced. A quick first pass should prioritize coverage over depth; touch every unit rather than staring at one stubborn area.

Pass two: build and clean candidates

When direct scanning slows down, add candidate notes to unresolved cells. Recalculate from the row, column, and box constraints rather than copying old assumptions. Then look for naked singles and hidden singles. Each placement should trigger immediate candidate cleanup in its peers, followed by another single scan.

If you are using selective notation, expand to full notation before relying on pairs or line patterns. Advanced deductions are only as reliable as the candidate map underneath them.

Pass three: use compact patterns

Next inspect boxes for pointing pairs or triples, then inspect units for naked pairs. These techniques remove candidates without guessing. After every elimination, return to singles. A pattern that removes only one small note can still be decisive if it exposes a forced placement elsewhere.

  1. Scan missing digits in boxes, rows, and columns.
  2. Calculate candidates and resolve naked singles.
  3. Scan units for hidden singles.
  4. Check box-line interactions such as pointing pairs.
  5. Check rows, columns, and boxes for naked pairs.
  6. Only then search for advanced patterns such as X-Wing.
  7. After any progress, restart the sequence from singles.

When the loop finds nothing

First audit the grid: confirm no entry is wrong and no candidate is stale or missing. Then focus on one digit across all nine boxes, or one constrained region where many lines intersect. If the puzzle is rated beyond your current technique set, use an instructional hint that names the strategy or clearly labels a solution-backed reveal. The aim is to learn the missing step, not conceal a guess.

Measure progress by clarity

Speed comes naturally after the workflow becomes familiar. At first, favor accurate explanations over fast input. Being able to say why a candidate was eliminated builds transferable skill and makes errors easier to correct. A completed puzzle is useful; a completed puzzle whose key steps you understood is much more valuable practice.

Frequently asked questions

Should I always use every technique in this order?

No. Treat the order as a priority loop. Skip a technique when the grid does not present it, and return to easier checks after any change.

What should I do before requesting a hint?

Audit recent entries, update candidates, scan every unit for singles, and check the most constrained boxes. A hint is most educational when you know which checks did not produce progress.