Petri Dish

Title: Petri Dish

Rating: 5/5

This is one of the hardest puzzles I've created, and it's essential that you use the last rule from the list below, an addition from other sum puzzles.

The official rules:

• The digits 1 through 9 appear in each row and each column exactly once.
• Digits in each shaded region must add to the indicated sum.   
• Squares with multiple colors contain a number that’s used in the sum for adjacent regions of each of those colors.
• Remember: numbers can repeat within a shaded region if that doesn't violate the first rule.
• Each number that appears in the five starting cells is the average of the entries in the edge-adjacent four cells (e.g., the 7 in row 5, column 5 (denoted (5,5)) is the average of the entries in cells (4,5), (6,5), (5,4), and (5,6)).