Odd/Even Sudoku is a 9x9 Sudoku variant in which some cells carry a marker: a circle means the cell holds an odd digit (1, 3, 5, 7 or 9) and a square means it holds an even digit (2, 4, 6 or 8). Unmarked cells are unrestricted. That is the entire rule — and because a Sudoku line contains exactly five odd digits and four even ones, a handful of markers constrains the board far more than their simplicity suggests.
What is Odd/Even Sudoku?
Odd/Even Sudoku constrains parity rather than value. Most variants tell you something about a digit's size (Thermo, Skyscraper), its sum with neighbours (Killer, Arrow, Sandwich), or its position (Column Indexer). Odd/Even tells you only whether a digit is odd or even, which is the least specific thing you can say about it — and yet it removes roughly half the candidates from every marked cell before you have placed anything at all.
The variant is also unusually approachable. There is no arithmetic, no geometry to trace, and no clue outside the grid to interpret. If you can tell an odd number from an even one, you can read every clue on the board immediately. That makes Odd/Even the gentlest of the five variants added in version 1.2.4, and a good first step for someone moving beyond Classic Sudoku.
Odd/Even Sudoku Rules
- Standard Sudoku rules: Each row, each column, and each 3x3 box must contain the digits 1 through 9 exactly once.
- Circles are odd: A cell marked with a circle must contain 1, 3, 5, 7 or 9.
- Squares are even: A cell marked with a square must contain 2, 4, 6 or 8.
- Unmarked cells are free: A cell with no marker may contain any digit. The absence of a marker says nothing about the cell's parity.
How the Parity Constraint Works
The digits 1 to 9 split five to four: 1, 3, 5, 7, 9 are odd and 2, 4, 6, 8 are even. Every row, every column, and every 3x3 box of a completed Sudoku contains all nine digits, so every one of those regions contains exactly five odd digits and exactly four even digits. That fixed ratio is the engine of the entire variant.
Each marker halves a candidate list
A circle cuts a cell from nine candidates to five; a square cuts it to four. On its own that is modest. Combined with ordinary elimination it is decisive: a cell that would otherwise be down to two candidates is resolved outright the moment one of them has the wrong parity. Most Odd/Even progress comes from exactly this — the marker breaking a tie that Classic logic left standing.
Regions have parity budgets
Because a region holds five odds and four evens, it can carry at most five circles and at most four squares. Whenever a region reaches one of those limits, every remaining cell in it is forced the other way:
- A row with five circles has spent its entire odd budget. The other four cells must hold 2, 4, 6 and 8 in some order.
- A row with four squares has spent its entire even budget. The other five cells must hold 1, 3, 5, 7 and 9 in some order.
Both cases hand you a complete parity map of the line for free, and they are common enough on medium and hard puzzles to be worth checking for on every region at the start.
Solving Strategies
1. Filter every candidate list before you start
Do one pass over the whole grid and strike the wrong-parity digits from every marked cell. This is mechanical, takes a minute, and turns the rest of the puzzle into ordinary Sudoku on a much thinner candidate set. Skipping it and checking parity cell by cell as you go is how people find Odd/Even harder than it is.
2. Count circles and squares per region
Walk the nine rows, nine columns, and nine boxes and note the marker counts. Any region at five circles or four squares gives you the parity of every cell in it. Even a region at four circles is useful: it tells you exactly one of the remaining cells is odd.
3. Place even digits first
There are only four of them, and every square marker on the board is competing for those four slots in its row, column, and box. Chasing the 2, 4, 6 and 8 through a region with several squares in it usually resolves faster than working the odds, where five digits compete for five or more slots.
4. Use parity to invalidate patterns, not just cells
Parity applies to techniques as well as to cells. A naked pair of {3, 4} in a circled cell is really a naked single on 3. A hidden pair whose two cells are both squares cannot involve an odd digit at all. Reading your usual patterns through the parity filter is where the variant's harder puzzles open up.
5. Keep the standard toolkit
Everything in our solving techniques library works here unchanged. Odd/Even does not introduce new techniques; it makes the existing ones fire earlier by shrinking the candidate space they operate on.
Mini Odd/Even Sudoku (6x6)
Mini Odd/Even brings the parity rule to a compact 6x6 grid using the digits 1 through 6 with 2x3 boxes. The split here is even: 1, 3, 5 are odd and 2, 4, 6 are even, three of each. Every row, column, and 2x3 box therefore holds exactly three odd digits and three even ones, so a region can carry at most three circles and at most three squares.
The balanced three-and-three split makes the counting arguments cleaner than on the 9x9 board, where the five-four asymmetry takes a little getting used to. A circle on a 6x6 grid cuts a cell from six candidates to three — a genuine halving — which makes the markers feel powerful immediately. Mini Odd/Even is free to play; the 9x9 version is part of the premium collection.
Tips for Beginners
- No marker means no restriction. An unmarked cell can be odd or even. This is the mistake almost every new Odd/Even solver makes at least once.
- Learn the budget: five odds, four evens. On a 9x9 line, always. It is the only number you need to memorise for this variant.
- Squares are worth more than circles. Four candidates instead of five, in a region with only four even slots to give.
- Do the parity sweep first. Filtering every marked cell up front costs a minute and saves twenty.
- Watch for a full even budget. Four squares in one region means every other cell in it is odd — a free parity map of the line.
- Start on Mini Odd/Even. The free 6x6 grid splits three and three, which makes the counting arguments obvious before you meet the five-four asymmetry.
Odd/Even proves that a constraint does not have to be complicated to be strong. Circles and squares say the least it is possible to say about a digit, but they say it about a lot of cells, and the fixed five-to-four ratio in every region turns that vague information into hard counting arguments. It is the variant that most rewards being systematic and least rewards being clever.