How to Solve Medium Sudoku Puzzles
Medium sudoku puzzles require more than the basic techniques used on easy grids. You'll still use scanning and elimination — but you'll need to apply them more carefully, and you'll encounter moments where a new technique is necessary to make progress. This guide covers exactly what that looks like.
What's Different About Medium Puzzles?
Medium puzzles typically have fewer starting clues than easy ones — around 27–32 pre-filled cells compared to 35+ for easy. Fewer clues mean fewer immediate deductions. You'll often exhaust the obvious naked singles and find that several cells still have two or more candidates.
The key difference: medium puzzles require you to consider each group (row, column, box) as a whole unit — not just individual cells. This shifts your thinking from "what goes in this cell?" to "where does this digit go in this group?"
Step 1: Exhaust Naked Singles First
Start the same way you would on an easy puzzle. A naked single is a cell where only one digit is possible after checking its row, column, and box. Go through every empty cell and apply elimination. Fill in any naked singles you find.
After filling each one, re-check the affected row, column, and box for new naked singles. Repeat until no naked singles remain.
On medium puzzles, this phase will take you part of the way — but not all the way. When naked singles run out, move to the next technique.
Step 2: Find Hidden Singles
A hidden single is the most important medium-puzzle technique. Here's how it works: look at a specific digit — say, 4 — and examine each row, column, and box that doesn't yet contain a 4. For each group, identify which empty cells could possibly hold a 4. If only one empty cell in that group can hold a 4 (because all other empty cells are blocked by an existing 4 in their row, column, or box), then that cell must be 4.
The hidden single is "hidden" because the cell might appear to have several candidates at first glance — but within the context of a specific group, only one location works for that digit.
How to find hidden singles:
- Pick a digit (start with the one that appears most on the board).
- For each incomplete row, column, and box, locate the empty cells.
- Cross off any empty cell that shares a row, column, or box with an existing instance of that digit.
- If only one empty cell remains in a group, place the digit there.
- Repeat for all nine digits.
Example: Row 5 (highlighted) is missing two digits: 7 and 8. Its two empty cells both look like candidates for 7 — but column 3 already contains a 7 elsewhere on the grid, which blocks the left empty cell. Only the right empty cell can hold a 7, so it must be 7. Note that the cell still has two candidates overall — this is what makes it a hidden single, not a naked one.
Step 3: Alternate Between Techniques
Medium puzzles are solved by cycling between naked singles and hidden singles. Finding a hidden single places a digit, which may create new naked singles, which in turn may reveal new hidden singles. The puzzle unravels progressively.
A good solving rhythm:
- Fill all naked singles.
- Scan all nine digits for hidden singles in rows, columns, and boxes.
- Fill any found, then return to step 1.
Step 4: Use Pencil Marks When Needed
On medium puzzles, pencil marks become more useful. When you can't immediately identify the answer for a cell, write the remaining candidates as small numbers inside the cell. This externalizes your working memory and makes patterns easier to see.
As you place digits, erase the corresponding pencil marks from all affected cells. When a pencil mark cell is reduced to one candidate, fill it in.
Common Stumbling Points
Stuck after naked singles? This is normal for medium puzzles. Switch immediately to hidden single scanning — don't try to force naked singles where none exist.
Missing hidden singles? Try scanning each digit through boxes rather than through rows and columns. The box perspective often reveals hidden singles that the row/column scan misses.
Making errors? Slow down and verify every placement explicitly. Medium puzzles punish sloppy elimination — one wrong digit can make the rest of the puzzle unsolvable.
Ready for the Next Level?
With naked singles and hidden singles, you can solve any medium puzzle. Practice until both techniques feel automatic before moving on to hard difficulty.