When to Start Using Pencil Marks (and When Not To)
Sudoku a Day Blog
Pencil marks, the small candidate numbers you write in empty cells, are one of the most debated topics in Sudoku. Some solvers swear by them from the first cell. Others never use them at all. The truth is somewhere in between.
What pencil marks are
When you are not sure which number goes in a cell, you can write all the possible candidates as small numbers in that cell. As you solve other cells, you cross out candidates that become impossible. Eventually, a cell with three candidates becomes a cell with one, and you have your answer.
In apps, this is usually called "notes mode." On paper, it is literally pencil marks, tiny numbers in the corners or center of each cell.
When you do not need them
On easy puzzles, pencil marks are usually unnecessary. Most cells can be solved by scanning and basic elimination. If you can look at a cell, check its row, column, and box, and find the answer, writing candidates first just slows you down.
Beginners sometimes fill the entire grid with pencil marks before solving anything. This takes a long time and creates visual clutter that makes the puzzle harder to read, not easier.
When they become essential
Medium and hard puzzles are where pencil marks become valuable. At these levels, you will encounter cells where scanning does not give you a clear answer. You need to track possibilities across multiple cells to find patterns like hidden singles or naked pairs.
Without pencil marks, you are relying on memory alone. That works for a while, but as the grid gets more complex, mistakes creep in. Clean pencil marks reduce errors and speed up pattern recognition.
How to use them efficiently
Do not mark every cell at once. Instead, use pencil marks selectively:
1. Mark cells with 2-3 candidates. These are the most useful. Cells with 5+ candidates are rarely helpful to mark early.
2. Focus on one region at a time. Mark candidates in a box or row where you are actively working, not across the entire grid.
3. Update immediately. When you place a number, go back and remove that number from all pencil marks in the same row, column, and box. Stale marks cause errors.
4. Look for patterns. Once you have marks in a region, scan for pairs (two cells with the same two candidates) or singles (a candidate that appears in only one cell in a row, column, or box).
The transition point
Most solvers hit a natural transition around medium difficulty. Easy puzzles feel fine without marks. Medium puzzles start requiring them occasionally. Hard puzzles and above need them consistently.
If you are not sure whether you need pencil marks yet, try this: solve a medium puzzle without them. If you get stuck more than twice, marks would have helped.
Common pencil mark mistakes
Two errors trip up most people when they start using marks:
Marking too many cells at once. Full-grid marking takes time and creates visual noise. Be selective. Focus on the area you are actively working on.
Forgetting to update. Every time you place a number, that number needs to be removed from marks in the same row, column, and box. Stale marks are worse than no marks because they lead to false conclusions.
Build the pencil mark habit gradually, and it will feel natural by the time you reach harder grids. Practice with a printable medium pack or in the Sudoku a Day app.
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