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Curious Cheetah

Odd Even Sudoku

Background

In addition to the standard Sudoku rules, all shaded cells must contain either only odd numbers or only even numbers, depending on the original clues.

Puzzle and Goal

An unsolved puzzle consists of a 9x9 grid containing nine 3x3 regions. Some of the cells have been shaded, and some of the cells (both shaded and unshaded) contain a number between 1 and 9.
The goal is to fill in all the cells so as to create a Latin Square.

Rules

The solved grid must satisfy the following conditions: