Even-Odd Sudoku: Rules and Solving Strategy

Understand what the parity markers mean

Even-Odd Sudoku follows the ordinary rule that every row, column, and 3 by 3 box contains 1 through 9 exactly once. Marked cells add a parity restriction. A common convention uses circles for odd digits and squares for even digits, though publishers may reverse the symbols or use shading instead. Always read the puzzle key. The even digits are 2, 4, 6, and 8. The odd digits are 1, 3, 5, 7, and 9. A parity marker does not tell you the exact value, but it removes nearly half the candidates immediately. Unmarked cells usually carry no extra restriction unless the instructions say that every parity cell is marked. Shapedoku relies on nine distinct shapes rather than numerical parity, so this is a separate variant. Still, Shapedoku's Notes and shape-by-shape scanning build the same habit of narrowing a cell before trying to place anything.

Use the fixed parity balance in every unit

Every complete row, column, and box contains four even digits and five odd digits because it contains the full set from 1 through 9. That fixed balance is often more useful than a single marker. If a row already has four confirmed even digits, every remaining empty cell in that row must be odd. If a box has four odd placements and two unfilled cells marked odd, only one of those markers can remain possible because the box needs exactly five odd digits in total. Count parity without confusing it with exact candidates. Two cells both marked even do not automatically form a pair because they may still use any two values from 2, 4, 6, and 8. However, if the box already contains 2 and 8, those two cells are restricted to 4 and 6 and do form a naked pair. Parity creates the frame; ordinary candidate logic supplies the exact digits.

Combine parity with sums, pairs, and missing digits

Focus on nearly complete units. If a row is missing 2, 5, and 7 and one empty cell is marked even, that cell must be 2, leaving 5 and 7 for the others. If a column is missing 1, 4, 6, and 9 and two cells are marked odd, those cells must take 1 and 9 in some order while the even cells take 4 and 6. This creates immediate subsets that may interact with boxes. Parity is also useful for checking candidate chains: an odd-only cell cannot serve as a link through an even candidate, however attractive the surrounding pattern looks. On paper, small O and E notes can keep the board readable. On a digital candidate grid, remove the wrong parity first, then apply row, column, and box restrictions. Do not place a value simply because its parity matches. A cell marked odd still needs one exact digit proven by the full Sudoku rules.

1. Confirm which visual marker means odd and which means even.
2. Remove even digits from odd cells and odd digits from even cells.
3. Count four even and five odd digits in every row, column, and box.
4. Use missing-digit lists to turn parity restrictions into exact candidates.
5. Look for pairs formed when only two even or two odd values remain.
6. Verify every placement against parity and all three standard Sudoku units.