The case notes
Count the odds to orient a parity line
A parity line alternates odd and even digits. We do not know either end of this line, but the row can tell us how the pattern starts. Watch a worked example, then try the idea in a puzzle.
Put it into practice
Which way does the line alternate?
A parity line alternates odd and even digits. We do not know either end of this line, but the row can tell us how the pattern starts.
O–E–O: two odds · E–O–E: one
Three cells could go odd, even, odd. Or even, odd, even. The first pattern uses two odd places; the second uses one.
Four odds used · one left
Every Sudoku row has five odd digits. Four are already outside this line: one, three, five and seven. There is room for only one more odd.
Even · Odd · Even
Odd, even, odd would make six odds in the row. Impossible. So the ends are even and the middle is odd.
r1c5 = 9
One, three, five and seven are already used. The middle must be the last odd digit: nine.
Read the transcript
A parity line alternates odd and even digits. We do not know either end of this line, but the row can tell us how the pattern starts. Three cells could go odd, even, odd. Or even, odd, even. The first pattern uses two odd places; the second uses one. Every Sudoku row has five odd digits. Four are already outside this line: one, three, five and seven. There is room for only one more odd. Odd, even, odd would make six odds in the row. Impossible. So the ends are even and the middle is odd. One, three, five and seven are already used. The middle must be the last odd digit: nine.
