Level 5 · Outside clues and specials

How to solve odd-even sudoku

Name: Odd Even Sudoku Explained in One Short Example
Uploaded: 2026-09-23
Duration: 15 s
Description: A four-cell row has a circle and a square. A 5 in the square breaks the rule because 5 is odd, and a 3 in the circle with a 4 in the square passes.

A gray circle holds an odd digit. A gray square holds an even digit.

Odd Even Sudoku Explained in One Short Example · 15 seconds

Odd-even sudoku marks some cells with shapes. A gray circle means the cell holds an odd digit, and a gray square means it holds an even digit. Normal sudoku rules still apply.

Each mark cuts a cell to five or four options before you start. The marks do the most work when you count how many odd and even cells are left in a row, column or box.

How setters write it

The same rule, worded the ways you’ll see it on puzzles.

Digits in gray circles are odd. Digits in gray squares are even.
Odd/even sudoku.
Shaded circles contain odd digits; shaded squares contain even digits.

Worth memorizing

There are five odd digits (1, 3, 5, 7, 9) and four even ones (2, 4, 6, 8).
So a box can hold at most four squares, and five circles force every odd digit into them.
Pair it with sums: an odd circle plus an even square always makes an odd total.

Solving tips

Count the evens

Each row, column and box has exactly four even digits. If four cells in a box have squares, every other cell in that box is odd.

Five circles use every odd

If a box has five circles, those cells hold 1, 3, 5, 7 and 9. No other cell in that box can be odd.

Finish a set of evens

If a row already has 2, 4 and 8 placed, any square left empty in that row must be 6.

Combine marks with sums

Two odd digits always add to an even number. If two circled cells form a two-cell killer cage, the cage total must be even.

A worked example: counting the evens in a box

We name cells by row and column, so row 1, column 1 is r1c1. In the top-left box, four cells have gray squares. r1c1 holds 2, r2c2 holds 4, and r3c1 and r3c3 are empty. The other five cells of the box are empty and unmarked. Column 1 has a 6 in r7c1. Row 1 has 1, 3 and 5 outside the box, and column 2 has a 9 below the box.

The squares at r3c1 and r3c3 must hold even digits. The box already has 2 and 4, so these two cells are 6 and 8 in some order.
r3c1 is in column 1, which has a 6 in r7c1. So r3c1 = 8 and r3c3 = 6.
A box holds exactly four even digits, and all four are now in the squares. So the five unmarked cells must hold the five odd digits: 1, 3, 5, 7 and 9.
r1c2 and r1c3 are two of those odd cells, and they are in row 1. Row 1 already has 1, 3 and 5. So r1c2 and r1c3 are 7 and 9.
Column 2 has a 9 below the box, so r1c2 can't be 9. r1c2 = 7 and r1c3 = 9.

Practice

1 of 2

Tap every digit that could go in the circle.

Select all that apply

2 of 2

Tap every digit that could go in the square.

Select all that apply

Reference table

Possible totals of two different digits, by their marks. Use it when two marked cells share a killer cage, sit on an arrow, or sit next to each other in a sum clue.
Two marked cells	Possible totals
Circle + circle (odd + odd)	4, 6, 8, 10, 12, 14, 16
Square + square (even + even)	6, 8, 10, 12, 14
Circle + square (odd + even)	3, 5, 7, 9, 11, 13, 15, 17

Going deeper

Using odd and even inside sums

A total is odd when it has an odd number of odd digits in it. Two odd digits make an even total. Three odd digits make an odd total. Even digits never change whether a total is odd or even.

So a three-cell cage with a total of 15 and two circled cells must have an odd third cell. The two circles add to an even number, and an even number plus an odd digit is the only way to reach 15. Checks like this cut candidates before you try any combinations.

Two-cell cages are the easiest case. A two-cell cage with an odd total must hold one odd digit and one even digit. So if one of its cells has a circle, the other cell is even, even if it has no mark.

Counting a row and a box together

A row holds five odd digits and four even ones. So does every column and box. If a row already has three even digits placed and one square left empty, that square takes the last even digit. Every other empty cell in the row is odd.

The count works across overlaps too. If a box needs two more even digits, and a row through the box can't hold any more evens, those two evens must go in the box's other two rows.

Look for rows where the marks settle everything. If a row has four squares, all four of its even digits are in those squares. Its five other cells are all odd, marked or not.

Smaller grids have a different count

In a 6x6 grid the digits are 1 to 6. That is three odd digits (1, 3, 5) and three even ones (2, 4, 6). The counting tricks still work, but the numbers change.

Always count from the digits the grid uses. A rule of thumb from a 9x9 grid can mislead you on a smaller one.

A 4x4 grid uses 1 to 4, so each row, column and box holds two odd digits and two even ones.

Common mistakes

Assuming unmarked cells are the other parity

An unmarked cell can hold any digit unless the rules say every odd or even cell is marked. Only use the count of five odd and four even to decide what an unmarked cell must be.

Reading the shapes backwards

Circles usually mean odd and squares usually mean even, but setters vary. Some puzzles use colors or shading. Read the puzzle's rules before you place anything.

Thinking odd and even split evenly

There are five odd digits and only four even ones in 1 to 9. A box can hold five odd digits but never five even ones. A row with four squares has all four of its even digits in those squares.

In mixed-rule puzzles

Odd and even marks work well with dot rules. Two digits one apart always have one odd and one even. So a white Kropki dot (usually the sign for consecutive digits) next to a circle means the other cell is even. A black Kropki dot joins digits where one is double the other. The pairs are 1 and 2, 2 and 4, 3 and 6, and 4 and 8, and every pair has an even digit. So a black dot can never join two circles. With killer cages and arrows, the table above shows which totals two marked cells can reach. Parity lines use the same odd and even idea along a line. Check the rules for which marks each puzzle uses.

What the video shows

Gray circles hold odd digits. Gray squares hold even digits.
5 is odd, so it can’t go in a square.
3 in the circle, 4 in the square.

Questions solvers ask

What do circles and squares mean in sudoku?

In odd-even sudoku, a gray circle marks an odd digit and a gray square marks an even digit. Check the rules, since some puzzles use other shapes or colors.