A Pencil-Mark Workflow That Actually Works

Pencil marks are the most common reason solvers get stuck. Not because they are hard to use, but because most people use them haphazardly. Half a grid marked, the other half ignored, candidates left over from ten placements ago. That is not a notation system. That is a mess.

A clean pencil-mark workflow is worth more than any single advanced technique. Here is the one I use, the one I teach, and the one that keeps medium and hard puzzles honest.

The rule: mark every cell, or mark none

Half-marked grids lie to you. You scan a cell, see one candidate written down, and place it. But the cell next door, which you never marked, might have had constraints you never noticed. The placement you just made was a guess wearing a costume.

Pick a moment in the solve. Before that moment, no marks. After it, every empty cell carries a complete candidate list. The transition is the only honest way to use them.

The four-step workflow

1. 1
   Pencil every empty cell

   For each empty cell, write the digits that could go there. Use small marks in the top portion of the cell. The set is whatever survives the row, column and box constraints.
2. 2
   Place every naked single you uncover

   Some cells will end up with only one candidate. Those are placements waiting to happen. Place them, and remember the digit you placed.
3. 3
   Sweep peers immediately

   Every time you place a digit, walk that digit's row, column and box. Erase it as a candidate from every cell that sees the new placement. This is the only step beginners skip, and skipping it ruins the marks.
4. 4
   Re-scan for new singles

   A sweep often collapses another cell to a single candidate. Keep placing and sweeping until the cascade stops.

Steps one and two are slow. Steps three and four are quick. Most of the work happens up front. After the first pass, the marks update themselves as you solve.

Two notation styles, pick one and stay

The positional style places each digit in the cell at the position it would occupy in a mini three-by-three grid. A 1 in the top-left corner, a 5 in the centre, a 9 in the bottom-right. You read marks by their location, not their value, which is fast once you adjust.

The list style writes candidates left to right, the way you would write a phone number. Slower to read but takes less space, which matters on paper.

Either works. Switching between them mid-puzzle does not. Pick one and stay there for the whole solve.

The cardinal sin: stale marks

Stale marks are candidates that should have been erased and never were. They corrupt every technique that comes after. A naked pair you find using stale marks is not really a pair. The forcing chain you build on those marks is not really forced.

The fix is discipline, not intelligence. Sweep peers the instant you place a digit. Treat the sweep as part of the placement, not a separate step. If you can teach yourself this one habit, your stuck rate on hard puzzles falls by half.

When to switch to digital

Paper erasers wear holes. Digital marks update faster and never lie about what is on the page. If you find yourself solving more than one puzzle a day, switching to a digital surface like our medium puzzle player is worth it. The marks behave the same way. Only the medium changes.

One last habit

Look at your marks before you reach for advanced techniques. Most "stuck" moments resolve themselves once the marks are clean. Naked and hidden singles hide inside untrustworthy marks. The technique you need is usually waiting for you to clean up first.

For a deeper look at notation as a tool, see the pencil marks strategy page, and the related when to switch to pencil marks. Try the workflow on an medium puzzle and see how much cleaner the solve feels.