All Sudoku Variants
9×9 · Constraint

Parity Lines Sudoku

Along a marked line the parity alternates — odd, even, odd, even — so neighbouring cells on the line are always one odd and one even.

5 61472

An example Parity Lines puzzle: the parity alternates along the line — odd, even, odd, even (1, 4, 7, 2).

Parity Lines Sudoku draws lines whose digits must alternate odd and even. Step along the line and the parity flips every cell: if one is odd, its neighbour is even, the next odd again, and so on. The digits themselves are free — only their odd/even pattern is fixed.

The rule: odd, even, odd, even

Pick any marked line and read it end to end. No two adjacent cells on it share a parity, so the line is a strict alternation of odd and even values, on top of all the usual Sudoku rules.

Solving strategy

  • Fix one, fix them all. A single known parity on the line sets the odd/even pattern for the whole line.
  • Halve the candidates. Each line cell is limited to {1,3,5,7,9} or {2,4,6,8} before any other clue.
  • Combine with the grid. The parity pattern often collides with a row, column or box elimination to pin a digit exactly.

Common mistakes

  • Reading it as all-odd or all-even. Parity alternates; it does not stay constant along the line.
  • Forgetting parity has five odds, four evens. The odd cells draw from a larger pool than the even ones.
  • Dropping the ordinary rules. Rows, columns and boxes still each need 1–9 once.

Can I play it here?

Not yet — Parity Lines Sudoku isn't one of the puzzle types SudokuStreak generates for now. But you can learn its rules above, and there's plenty here to sink your teeth into meanwhile: