Even-Odd Sudoku – Medium

Even-Odd Sudoku

Even-Odd Sudoku is a classic 9x9 Sudoku with additional markings for even and odd numbers. In this variant, marked squares indicate even numbers, while marked circles show odd numbers. The basic rules of standard Sudoku remain unchanged.

The additional rule is simple but effective: A marked cell allows only numbers of the matching parity. Even numbers are 2, 4, 6, and 8. Odd numbers are 1, 3, 5, 7, and 9.

Basic Rules

• Each row contains the numbers 1 to 9 exactly once.
• Each column contains the numbers 1 to 9 exactly once.
• Each 3x3 block contains the numbers 1 to 9 exactly once.
• A cell marked as even can only contain 2, 4, 6, or 8.
• A cell marked as odd can only contain 1, 3, 5, 7, or 9.
• Unmarked cells have no additional parity restrictions.

Solve Strategies

1. Use Parity as a Candidate Filter

The marking can immediately halve the candidates. Instead of 1 to 9, only 2, 4, 6, and 8 are possible in an even cell.

In the following example, we consider row 2, column 1. This cell is marked as even.

In row 2, the missing numbers in the open spots are 5 and 6. The cell in row 2, column 1 is marked as even. The 5 is odd and thus excluded. The only remaining candidate is 6.

2. Sort Even and Odd Cells Early

Even cells can only be 2, 4, 6, or 8. Odd cells can only be 1, 3, 5, 7, or 9. This simple separation is often the fastest way to reduce candidates.

3. Combine Parity with Blocks

If multiple marked cells are in a 3x3 block, you can quickly see which numbers still have space there. An odd-marked cell can, for example, never contain 2, 4, 6, or 8, even if those numbers are still possible in row or column.

Typical Solving Process

1. Mentally mark all even and odd cells.
2. Reduce candidates in even cells to 2, 4, 6, and 8.
3. Reduce candidates in odd cells to 1, 3, 5, 7, and 9.
4. Combine these restrictions with row, column, and 3x3 block considerations.
5. Enter numbers only when, after all checks, only one possibility remains.

Common Mistakes

• Guess too early instead of using the extra rule as a safe exclusion.
• Only check rows and columns and overlook the special marking of the puzzle.
• Enter a number that fits locally but violates the special rule.
• Do not update candidates after each new entry.
• Misread a marking or apply it to the wrong cells.

Tips for Beginners

• Start like a standard Sudoku with well-filled rows, columns, and regions.
• Then check the special rule specifically. Often, early safe exclusions are found here.
• Always consider: Which numbers are truly allowed and which are excluded by a rule?
• Enter a number only when it can be definitively derived.
• If stuck, change perspective: from rows to columns, regions to the special rule, or from individual cells to candidates.

Even-Odd Sudoku is particularly beginner-friendly because the additional rule is easy to spot. However, never rely solely on the markings: an entry must always fit the row, column, and block as well.