How to Use Pencil Marks and Candidates in Sudoku

Pencil marks are the bridge between beginner and advanced Sudoku. Up to a point you can solve in your head by scanning, but harder grids hold too many possibilities to track mentally. That's where candidates come in. You write the possible digits into each empty cell, turning a memory exercise into a pattern-spotting one. Almost every technique past the basics (pairs, triples, X-Wings) needs them. Here's how to use them well, because sloppy pencil marks cause more wrong turns than any other single thing.

What pencil marks are

A pencil mark (also called a candidate or just a "note") is a small digit written in a cell to show that the digit is still legally possible there. A cell might carry {2, 5, 8}, meaning those three are the only numbers that fit given its row, column, and box. As you solve, candidates get eliminated until a cell drops to one, which is a naked single.

On screen, our boards handle this for you with a notes mode. On paper you write tiny digits in the corners. Either way, the idea is identical.

When to start using them

This is the part people get wrong, so I'll be blunt: don't pencil-mark too early. On easy and early medium puzzles, candidates are clutter. Scanning and forced cells will carry you, and filling a grid with notes you don't need just slows you down and makes the board hard to read.

The right moment is when scanning stalls. You've swept all nine digits and nothing new is forced. That's almost always on hard puzzles and up. At that point, candidates stop being clutter and start being the whole game.

How to mark cleanly

Good notation is mostly about consistency:

• Mark all candidates, or none in that cell. A half-filled cell is a trap. If you note candidates for a cell, note every legal digit, or you'll trust a deduction that's missing an option.
• Keep them in the same place. Same corner, same order, every cell. When notes are tidy, your eye can scan a whole row of candidate lists in one pass.
• Erase the instant a candidate dies. This is the big one. Every digit you place removes that digit as a candidate from its row, column, and box. Clear those immediately. A stale candidate you forgot to erase is the number one cause of "the logic broke," and it didn't; your notes did.

What candidates unlock

Once the grid is marked, techniques you couldn't see before become visible:

• Hidden singles. Scan a unit for a digit that appears in only one cell's candidates. That cell is solved, even with other candidates listed.
• Naked pairs. Two cells in a unit sharing the same two candidates let you erase those digits from the rest of the unit.
• Triples and beyond. The same grouping logic at larger sizes, plus the advanced techniques like X-Wing that read patterns across multiple units.

None of these are findable without candidates. That's why pencil marks aren't optional at the higher levels. They're the lens that makes the patterns appear. The naked and hidden singles guide walks through each move with the candidate grids in place.

Digital vs paper

Digital and paper pencil marks differ in one practical way. On paper, you do all the bookkeeping yourself, adding candidates and, crucially, erasing dead ones. It's more work, but it keeps you fully aware of the grid's state. Our digital notes mode can auto-manage candidates, which is faster, though some solvers find that doing it by hand sharpens their eye. Try both and see which suits you.

One habit translates either way: before you trust an advanced deduction, glance back and confirm the candidates it relies on are actually current. Thirty seconds of checking beats a restart.

A simple practice routine

Take a hard puzzle. Solve by scanning until you stall. Only then, fill in complete candidates for every empty cell. Now hunt, singles first, then pairs. You'll feel the puzzle open up the moment the patterns become visible, and you'll build the instinct for when marks are worth the effort.

For the bigger picture of where pencil marks fit among every other technique, see the complete strategy guide. Then put it to work on a real grid.