Goal

Solve the sudoku puzzle by filling in each cell with a digit from 1-9 (or 1-5/1-7 for smaller puzzles). No digit can be repeated within the zones enclosed by thick black lines.
The zones have been gerrymandered so a majority of zones (those withed dashed lines) have a larger even sum than odd sum.

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Solve the sudoku puzzle by filling in each cell with a digit from 1-9 (or 1-5/1-7 for smaller puzzles). Use the following constraints to find the unique solution.

Each row and column contains each digit exactly once. No digit can be repeated within the zones enclosed by thick black lines, but these zones will generally not be large enough to contain all of the digits.

Even though the total sum of even digits is less than the sum of odd digits, the zones have been gerrymandered so a majority of zones have a larger even sum than odd sum.

In zones with dashed lines dividing cells, the sum of the even digits will exceed the sum of the odd digits. In zones with solid dividing lines, the sum of odd digits exceeds the even sum.

Each row and column contains each digit exactly once. No digit can be repeated within the zones enclosed by thick black lines, but these zones will generally not be large enough to contain all of the digits.

Even though the total sum of even digits is less than the sum of odd digits, the zones have been gerrymandered so a majority of zones have a larger even sum than odd sum.

In zones with dashed lines dividing cells, the sum of the even digits will exceed the sum of the odd digits. In zones with solid dividing lines, the sum of odd digits exceeds the even sum.

Don't forget that zones do not contain all of the digits. Familiarity with basic soduku solving techniques is good, but advanced strategies are not needed and often not possible without 3x3 blocks.

Look for zones that are almost complete to see if they require a specific digit to make evens or odds win.

The largest and smallest digits are most likely to cause problems. Check if an 8 or 9 would be too much for a zone, or if something more than 1 or 2 is needed.

Remember that successful gerrymandering means most of the odd zones have way too many odd numbers, so they are less likely to produce useful contradictions.

Once you can eliminate any possibility, check if that forces something else.

Look for zones that are almost complete to see if they require a specific digit to make evens or odds win.

The largest and smallest digits are most likely to cause problems. Check if an 8 or 9 would be too much for a zone, or if something more than 1 or 2 is needed.

Remember that successful gerrymandering means most of the odd zones have way too many odd numbers, so they are less likely to produce useful contradictions.

Once you can eliminate any possibility, check if that forces something else.