Snyder Notation: The Two-Pen Method, Explained

Step 1: The Core Marking Rule

The foundational rule of Snyder notation is to write a candidate digit in a cell's corner only when you have confirmed it can appear in exactly two or three cells within the same 3x3 box. You make this confirmation by scanning the box for that digit's possible positions. If a digit can only go in two or three cells within that box, you place a small notation of that digit in the top-left corner of each of those cells. This creates what are often called Snyder marks. The purpose is to track the limited placement options for each digit within a confined area, which often leads directly to the next logical step. Most cells will have no corner marks at all, keeping the puzzle visual field very clean.

Step 2: The Two-Pen Habit

A critical best practice is to use two distinct writing implements: one for confirmed Snyder corner marks and another for entering final solved digits. Many solvers use a sharp pencil for the small corner pencil marks and a pen for the final answer. This physical distinction reinforces the mental separation between provisional candidates and definite placements. It also prevents you from accidentally treating a corner mark as a solved cell. As you scan boxes and place corner marks, you might simultaneously spot a cell that can only hold one possible digit—a Naked Single. You would then use your pen to write that final digit large in the center of the cell.

Step 3: Solving from Corner Marks

With Snyder marks in place, you start solving. Look for two primary patterns. First, a Naked Single: a cell that, after considering all row, column, and box constraints based on your corner marks and given digits, has only one possible candidate remaining. Second, a Hidden Single: a digit that, within a row, column, or box, can only go into one specific cell, even if that cell has multiple corner marks. Solving these singles will place new digits. Each new placement allows you to perform candidate elimination, removing that digit as a possibility from its row, column, and box. This often creates new opportunities to apply the Snyder marking rule in other boxes.

• After placing a new digit, immediately check all affected boxes to see if you can now add new Snyder corner marks.

Step 4: When to Graduate to Full Candidates

Snyder notation is designed for the early and middle game. There comes a point where placing new corner marks no longer yields progress; the puzzle stalls. This is the signal to graduate to full candidate notation. In full notation, you list all possible digits for every empty cell, typically as small numbers filling the cell. Switching to full pencil marks reveals more advanced patterns like Hidden Pairs or X-Wings that are invisible with only corner marks. The transition is strategic: you maintain a clean grid for as long as possible, then expand your data only when necessary to crack the puzzle's harder constraints.

Step 5: Avoiding the Common Failure Mode

The most common mistake with Snyder notation is abandoning it too early and filling every cell with full candidates from the start. This creates visual noise, making it harder to spot the simple interactions Snyder notation highlights. Another error is marking a digit in a corner before confirming it is limited to two or three cells in its box, which pollutes the grid with inaccurate data. Sticking to the disciplined, two-pen method keeps your logic chain clean and your focus on the most productive eliminations. Our hint engine finds that players who skip to full notation prematurely often miss the straightforward singles that Snyder marks make obvious.

Putting It All Together: A Generic Walkthrough

Imagine starting a puzzle. You scan each 3x3 box, and in one box, you find that the digit 7 can only go in two specific cells. You place a small '7' in the corner of each. You repeat this for other digits and boxes. Soon, you notice a cell whose row, column, and box collectively eliminate all digits except for a 3. This is a Naked Single, so you pen in the 3. This new 3 eliminates '3' as a candidate elsewhere. In another box, this elimination now confines the digit 9 to just two cells, so you add '9' to those corners. You continue this cycle of marking and solving until no new corner marks lead to a placement. At that stall point, you fill in the full candidate list for remaining cells to find the next advanced technique, like a hidden pairs pattern, and complete the puzzle.