Sudoku Pencil Marks

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Published April 29, 2026 · Updated October 20, 2026

Pencil marks are the small digits you write in an empty square for the answers it can still take. How many you write is a real choice. Four moves into a Hard board from our generator, every candidate comes to 176 small digits in 51 squares; marking only the digits that are down to two places in their box comes to 26. We make these puzzles, so we can measure when each approach pays, and the answer depends on the level you play.

What are pencil marks in sudoku?

A pencil mark is a candidate: a digit that no square in the same row, column or box holds yet, so it could still be the answer. Solvers also call them notes, candidates or pencilmarks, and all four mean the same thing. On paper they go in small and light so they can be rubbed out. Sudopedia, the solvers’ wiki, describes them as “pencilled in small digits in the edges of the cell, or placed as small dots in a 3x3 pattern, each position representing a digit” (Sudopedia: Pencilmark).

Our games draw them by position: each digit has its own spot in a three-by-three grid inside the square, 1 at the top left, 5 in the middle, 9 at the bottom right. It is worth copying on paper. With every 5 in the same spot, you can see which squares of a row still hold a 5 without reading a single digit.

Full candidates or corner marks: which should you write?

Full candidates means every possible digit in every empty square. It is what Start Notes writes in one press, and what most of the technique guides on this site draw. Everything from a naked pair up is read from full marks, because a pair is a fact about two squares and only full marks describe squares. The cost is the writing: by hand, 176 digits on the board above, each to be crossed out later.

Corner marks are the lean style. You note a digit only in a box where it is down to two places, in the corners of those two squares, and leave the rest to scanning. The style is widely called Snyder notation, after Thomas Snyder, World Sudoku Champion in 2007, 2008 and 2011 (Wikipedia); one guide sums it up as marking “digits that appear in two or sometimes three cells inside a 3×3 box” (Sudoku Challenges). Snyder himself wrote in April 2025 that names like “Snyder notation” and “Nishio chains” “have some of the bits right but not the essence” of what their namesakes did (Grandmaster Puzzles), so here we just call the style corner marks. On the board above, both styles show box 6’s 2s pinned to column 7: in 26 corner marks, or among 176 full ones.

The gap between the two depends on the level. We counted both at the first move of 200 boards from each of our levels:

Medians at the first move of 200 boards per level, dealt by the generator behind our level pages, October 2026. Full candidates are what Start Notes writes. Corner marks count both marks of every digit that has exactly two places in its box.

The harder the board, the more full marks there are to write and the fewer corner marks. A sparse grid pins few digits to two squares, so corner marks thin out at exactly the levels where marks matter most. They are a good scanning aid on Easy and Medium. From Hard up, write full marks, or let Start Notes write them.

Do you need pencil marks on Easy and Medium puzzles?

Not on ours. Our Easy and Medium boards are dealt only if naked and hidden singles finish them, so every move is a single. A hidden single can be found by cross-hatching, sweeping one digit’s rows and columns across a box, without writing anything down. A naked single means counting the digits a square sees, which you can do in your head.

More to the point, on those levels the marks never know anything the digits don’t. Every mark that goes is struck by a digit you placed, and the board shows that digit. We played 200 boards of each level, always taking the simplest move, and on none of the 400 did an answer show up in full marks before the digits alone could show it.

That changes on Hard, where 23 of 200 boards needed a locked candidate, and on Expert, where 68 of 200 needed a locked candidate or a naked pair. On every one of those 91 boards, at least one answer could be seen only in the marks: 44 such answers on the Hard boards, 178 on the Expert ones. So start writing marks when a full round of scanning finds nothing. On about one Hard board in nine and one Expert board in three, the marks are the only place the next answer shows.

Why write marks if the digits are already on the board?

Because the marks hold what the digits can’t. Here is the same Hard board at its fifth move, with no single left. In box 6 the 2 can only go in R4C7 or R5C7, both in column 7. So column 7’s 2 is in box 6, and the 2s in R7C7 and R8C7 go. That is a pointing pair, one of the two kinds of locked candidates.

Now read R8C7 the way you would without marks. Row 8 holds 4, 9 and 7; column 7 holds 7, 3, 6 and 8; box 9 holds 1, 7 and 8. None of them is a 2 or a 5, so from the digits alone R8C7 could be either. What settles it is a deduction, and the marks are the only place it was written down. Place the 5 and singles finish the board.

How do Notes and Start Notes work in our games?

The pencil-mark buttons work the same way on our classic sudoku, its level pages, the daily sudoku and 17-clue sudoku:

• Notes switches the number buttons, and the 1 to 9 keys, from answers to marks. A digit adds its mark to the selected square, or takes it away if it is already there. Only an empty square takes marks. Press Notes again to go back to answers.
• Start Notes fills every empty square with the digits its row, column and box allow, replacing any marks already there. One Undo takes back the whole fill.
• Place a right digit and the game removes it from the marks of every square in its row, column and box. A wrong digit turns red, adds one to the mistake count and leaves every other square’s marks alone.
• Erase clears the selected square, answer and marks alike.

The themed games, such as Christmas sudoku, call the fill button Auto Notes, and it works the same way. Kropki sudoku has Fill, which applies the dots as well as the houses. Our other variant games have Notes but no fill, so there the marks, and the variant’s extra rule, are yours to write. The Sudoku Helper fills in every square’s marks on its first Next Hint and keeps them current after each step, and the Sudoku Trainer sets each position with every pencil mark showing.

Why do pencil marks go wrong?

Three ways, and each one makes a false pattern look real:

• A mark you never wrote. Leave one digit out of a square and it can pass for a two-candidate square; read a pair off it and you cross out an answer that was right. Partial marks are fine for scanning; read patterns only from complete ones.
• A mark you never struck. A placed digit sees 20 other squares, and its mark has to come out of every one of them still empty. On paper, that is where marks go stale. Our games do it for you, but only for a right digit.
• A mark written from a wrong digit. Start Notes trusts the digits on the board, wrong ones included. On the Hard board above, 125 of the 176 marks are wrong answers. Put any one of them in its square and press Start Notes, and two or three squares lose their real answer: the ones in that row, column and box whose answer is the digit you placed.

Our guide to sudoku mistakes covers what our games do with a wrong digit, and how to track one down on paper.

Which sudoku techniques need pencil marks?

Every technique past the singles. On our levels that means the locked candidates, pointing pairs and box/line reduction, on Hard and Expert, then naked pairs on Expert. Nothing else is ever needed there. The rest, from hidden pairs and the X-Wing to the XY-Wing and simple colouring, turns up only on our Evil and Extreme puzzles. Each one is a rule for crossing out marks, and our guide to sudoku techniques puts them in order.