How to solve Even-Odd Sudoku

Seeing it. A square has only four candidates and a circle has five, so they're often solved long before a plain cell would be. A square is solved when its row, column and box between them show three of the four even digits. A circle needs four of the five odd ones. A plain cell needs eight different digits. In the diagram, the green cell, row 7, column 8, is a circle.

Using it. Look at what its row, column and box already hold. They show 1, 3, 5 and 7, marked blue, so the green cell is the fifth odd digit, 9. Go round every square and circle this way first. Each one you solve shortens the lists of the cells around it.

Seeing it. An even digit can't go in a circle and an odd digit can't go in a square. So when you ask where a digit can go in a row, column or box, you only count the cells of the right kind. In the diagram, row 4 needs an 8. Cross out its circles, marked purple, then every cell that shares a row, column or box with an 8, marked blue.

Using it. Only row 4, column 6 is left, so it's 8. Pointing pairs and claiming work the same way, just on the shorter list of cells the parity leaves you.

Seeing it. Every unit has four even digits and five odd ones. Count the even digits you can see in the unit: the squares, plus any even digits already placed. Four even digits means they're all used up, and five odd ones means the same for the odds. In the diagram, row 1 has four squares, marked purple.

Using it. With four evens, every plain cell left in the unit is odd. With five odds, every plain cell is even. The green cells, row 1, column 6 and row 1, column 9, lose their even candidates. Each plain cell is in three units, so check all three. If any one of them forces the cell to be odd, it only has odd candidates left.

A unit with one plain cell left is a special case. The cell takes whatever parity is missing: even if the other eight cells include three evens, odd if they include four.

Seeing it. A row and a box share three cells. Take those away and each has six cells left. The row had four even digits to begin with, and so did the box, so the six cells left in the row hold as many even digits as the six left in the box. A column against a box works the same way. In the diagram, the six row cells are purple and the six box cells are blue and green.

Using it. Count the even digits you can see in each set, then ask what the plain cells have to be. Row 2's six cells show two even digits, the 2 and the 8, and one plain cell, so the row has two or three. The box's six cells show three, two squares and the 4, and one plain cell, so it has three or four. The two counts must match, so each has three. The green cell, row 3, column 6, is odd and loses its 2 and 6. Row 2's plain cell is even.

Seeing it. The squares in a unit share out only four digits, 2, 4, 6 and 8, so groups appear quickly. Look for two squares that can only be one pair of digits, or three that can only be three. The circles share out five digits, so look there too. In the diagram, column 8 already has a 4 and an 8, so the two squares, row 4, column 8 and row 8, column 8, can only be 2 or 6.

Using it. They take those digits between them, so remove them from every other cell in the unit. Plain cells count too. The green cells, row 5, column 8 and row 9, column 8, lose their 2, and row 5, column 8 loses its 6 as well.