Snyder Notation: The Fast Pencil Mark Method for Sudoku

Snyder notation is a light pencil-marking method where you write a digit into a box only when it has exactly two possible cells left there, and you mark nothing else. You find those pairs by cross-hatching: for each digit, scan the rows and columns that block a box and see where it can still go. One spot means you fill it in, two spots means you mark both, three or more means you leave it alone for now.

It is named after Thomas Snyder, a multiple World Sudoku Championship winner who popularised it for speed solving. Many easy and medium puzzles can be finished with Snyder marks plus row and column scanning, and the marks are fast to write because each box usually holds only a handful.

Puzzle 201002 from the Sudoku Royale library. Givens (row by row, dots are blanks): .....2.6.....4..5..3.59.8....4..61.5..9.2.67.1..3.4.8.26.435...7.3................ The marks are computed from the givens only: every box single is placed first, then each digit with exactly two spots in a box is marked. We draw the marks in candidate position; on paper most people write them small in the top corners of the cell.

How to write Snyder marks

1. Take one digit. Start with 1 and go through every box, or start with whichever digit has the most givens, since it blocks the most cells.
2. Cross-hatch each box. For a box that does not have the digit yet, cross out (in your head) every row and column that already contains it, and every filled cell. Count what is left.
3. One spot: fill it in. That is a hidden single in the box. Placing it can create new singles, so keep going.
4. Two spots: mark both. Write the digit small in both cells. That pair is a fact about the box that stays true for the rest of the puzzle.
5. Three or more: write nothing. Come back later when more digits are placed.
6. Clean up as you go. When you place a digit, erase its marks from that box. If the new digit blocks one cell of a pair in another box, the other cell of that pair becomes a single.

In the example, the first pass over the givens places 14 digits. They include a 3 in R2C6 and 6s in R2C4, R6C3 and R3C1. It also leaves 19 pairs, which is all the marking this puzzle needs at this stage.

What the marks tell you

Snyder marks are sparse, so the patterns in them are easy to read.

• Two digits sharing the same two cells. In box 5, the 1 and the 8 can both only go in R5C4 or R5C6. Those two cells must be 1 and 8 in some order, and they hold nothing else. Box 6 shows the same thing with 2 and 9 in R6C7 and R6C9. Here those are also the last empty cells of their boxes, but the rule holds in any box: two digits marked in the same two cells form a hidden pair.
• A pair on one line points. The 3 of box 3 is marked in R1C7 and R1C9, both on row 1. Whichever cell it is, row 1 gets its 3 inside box 3, so no other cell in row 1 can be 3. This is pointing, and with Snyder marks you see it for free.
• Pairs help row and column scans. In row 3, the 4 can only go in R3C8. Box 1's 4 is marked on row 1 (R1C1 and R1C2), box 2 already has a 4, and box 3's 4 is marked in R1C7 and R3C8, which rules out R3C9. The same scan puts the 5 of row 8 in R8C7: box 7's 5 is marked on row 9, box 8 has a 5, and box 9's 5 is marked in R8C7 and R9C7.

Snyder notation vs full candidates

Full candidate marking writes every digit that could still go in each cell. It shows everything, but on this puzzle it would mean 40 cells of notes, many with four or more digits, and every placement forces a round of erasing.

Snyder marks are a small subset of that. The trade-off is that they only see box information. In this position, R2C1 can only be 9 once you check its row, column and box together. None of the Snyder marks point at it, because R2C1 is a naked single, a cell-based fact, and Snyder only records where a digit can go inside a box. Fast solvers handle this by checking the few cells in a row or column that are nearly full, which is quick without notes.

When to switch: once cross-hatching stops producing singles and the pairs are not giving you anything new, fill in full candidates. Pairs, triples, X-Wings and everything beyond them need the complete picture, including pages like the skyscraper and unique rectangle. Our pencil marks guide covers full marking.

Why speed solvers use it

Writing fewer notes saves time, but the bigger gain is that Snyder marks never go stale in a misleading way. A pair in a box stays a pair until one of its cells is filled, so you rarely erase. That makes it a good fit for timed play, as covered in our guides on how to solve sudoku faster and speed solving.

For the full order of techniques, from singles to chains, see our list of sudoku techniques in learning order and the overview of advanced sudoku strategies.