Medium Sudoku
Play it here or print a sheet. The level where singles stop being enough and one new idea — the naked pair — carries you the rest of the way.
Print a sheet of 6
Six moderate puzzles and their answers, on separate sheets so a puzzle cannot be spoiled by the page it is on.
The puzzles
Puzzle 1 — Moderate 5 8 9 1 3 9 2 8 1 2 9 7 6 7 4 5 8 9 8 6 8 9 5 3 5 8 9 2 Puzzle 2 — Moderate 8 1 9 5 4 3 8 6 4 7 1 5 3 4 8 2 3 7 2 7 5 6 4 9 7 2 5 8 Puzzle 3 — Moderate 4 5 6 5 1 7 2 9 6 8 7 1 4 7 5 6 8 9 2 3 9 1 2 9 5 3 Puzzle 4 — Moderate 9 3 5 4 5 8 7 8 7 4 2 7 8 9 6 1 7 1 5 6 3 2 2 1 5 6 8 9 6 Puzzle 5 — Moderate 6 2 3 8 5 1 9 4 4 9 3 4 8 3 1 6 5 7 6 8 6 8 9 5 3 5 1 6 Puzzle 6 — Moderate 3 4 8 6 9 7 6 4 7 3 5 4 5 3 8 6 7 5 2 4 5 3 9 1 5 2 1 3 4 2
The answers
Puzzle 1 — Moderate (answer) 5 8 4 6 3 9 1 2 7 7 3 9 1 4 2 6 5 8 1 2 6 5 8 7 9 4 3 9 5 7 3 6 8 2 1 4 2 1 8 7 9 4 3 6 5 4 6 3 2 5 1 8 7 9 3 9 1 4 2 5 7 8 6 8 4 2 9 7 6 5 3 1 6 7 5 8 1 3 4 9 2 Puzzle 2 — Moderate (answer) 7 2 3 8 1 6 9 5 4 4 9 1 5 2 3 8 7 6 6 8 5 9 4 7 2 1 3 1 5 7 3 8 2 4 6 9 3 4 9 7 6 5 1 8 2 2 6 8 1 9 4 5 3 7 8 3 4 2 7 1 6 9 5 5 1 6 4 3 9 7 2 8 9 7 2 6 5 8 3 4 1 Puzzle 3 — Moderate (answer) 9 3 2 7 1 4 5 6 8 4 5 6 2 9 8 7 1 3 1 7 8 5 6 3 2 4 9 5 2 4 1 3 6 9 8 7 3 1 9 4 8 7 6 5 2 6 8 7 9 5 2 1 3 4 2 4 3 6 7 5 8 9 1 7 6 1 8 4 9 3 2 5 8 9 5 3 2 1 4 7 6 Puzzle 4 — Moderate (answer) 1 8 7 9 4 2 3 6 5 4 2 6 1 3 5 8 9 7 3 9 5 6 8 7 1 4 2 6 4 3 2 5 1 9 7 8 9 5 8 7 6 4 2 3 1 7 1 2 8 9 3 6 5 4 5 6 4 3 2 8 7 1 9 2 3 1 5 7 9 4 8 6 8 7 9 4 1 6 5 2 3 Puzzle 5 — Moderate (answer) 8 1 9 6 2 4 5 7 3 2 3 4 9 5 7 8 1 6 7 5 6 1 8 3 2 9 4 1 6 5 4 9 2 7 3 8 4 9 8 3 7 1 6 2 5 3 7 2 5 6 8 9 4 1 6 8 1 7 3 9 4 5 2 9 2 3 8 4 5 1 6 7 5 4 7 2 1 6 3 8 9 Puzzle 6 — Moderate (answer) 9 7 3 4 1 5 8 2 6 8 5 1 6 9 2 4 3 7 2 6 4 8 7 3 1 5 9 4 2 7 3 6 8 5 9 1 1 3 8 2 5 9 6 7 4 6 9 5 1 4 7 3 8 2 7 4 2 5 3 6 9 1 8 5 8 6 9 2 1 7 4 3 3 1 9 7 8 4 2 6 5
The naked pair, and why it is the step up
Two squares in the same row, column or box that each hold exactly the same two candidates. Between them they will use both of those digits, in some order — which means no other square in that unit can hold either one.
You do not learn which square gets which digit, and that is the point that trips people up. A naked pair places nothing. What it does is remove candidates elsewhere, and it is those removals that usually turn some other square into a single.
It is the first technique that is genuinely about eliminating rather than placing, and getting comfortable with it is the difference between finishing medium puzzles and abandoning them.
When to stop looking for singles
Not too early. A medium puzzle usually opens with a run of singles, and only after those are exhausted does it need the new idea. Reaching for a pair while singles remain is slower, not cleverer.
The signal that you have run out is a full sweep — every box, then every digit through every row and column — that places nothing. At that point pencilling in candidates is worth the time it costs, because a naked pair is very hard to spot without them.
Pencil marks are why these print with generous squares. A grid sized for a printed digit has no room for six small ones, and a medium puzzle you cannot annotate is a medium puzzle you will not finish.
What comes after it
Once a pair has removed some candidates, go back to singles immediately. The grid has changed and squares that were ambiguous a moment ago may now be forced.
That loop — singles until stuck, one elimination, singles again — is the whole rhythm of solving, and it is exactly the loop the grader on this site runs to decide which level a puzzle belongs to.
If the loop stalls with no pair to be found, the puzzle is a level above this one. It is not stuck, and it does not need a guess.
Common questions
What is a naked pair in Sudoku?
Two squares in one row, column or box that hold exactly the same two candidates. They will use both digits between them, so no other square in that unit can hold either — it removes candidates rather than placing a digit.
Do I need to write pencil marks for medium Sudoku?
For most people, yes. A naked pair is very hard to see without candidates written in, which is why these puzzles print with squares big enough to annotate.
Why does my medium puzzle stall after a few moves?
That is the level working as intended: the opening singles run out and a naked pair is needed to open it again. Sweep for pairs, apply the eliminations, then go straight back to looking for singles.