Balloon

Title: Balloon

Rating: 1/5

If only to showcase that the mild alteration from the last sum puzzle wouldn't always lead to something very very hard, I offer this week's puzzle, which may be cause for celebration at its ease.  But remember: don't forget about the last rule from the list below.

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 eight starting cells is the average of the entries in the edge-adjacent four cells (e.g., the 7 in row 3, column 2 (denoted (3,2)) is the average of the entries in cells (3,1), (3,3), (2,2), and (4,2)).

Singapore Sling

Title: Singapore Sling

Rating: 3/5

When I was a tween (not that such a term existed at that point), I can remember my mom coming home from a party talking appreciatively about this drink.  My sister turns 40 today, so perhaps she'll enjoy one of these.

The colors in the puzzle are meant to evoke the cherry brandy, Cointreau, pineapple juice, and lime juice contained therein.  If you're planning to mix one, don't forget the gin, Bénédictine liqueur, grenadine, and bitters.

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 (denoted by +) or multiply to the indicated product (denoted by *).   
• Squares with multiple colors contain a number that’s used in the sum/product for adjacent regions of each of those colors.  
• Remember: numbers can repeat within a shaded region if that repetition doesn't violate the first rule.

Balance

Title: Balance

Rating: 3/5

If you look at it just right, you'll see how the title of the puzzle arises from how the regions appear as blocks built upon and supporting each other.

The official rules:

• The digits 1 through 9 appear in each row and each column exactly once.
• Digits in each shaded region must multiply to the indicated product.   
• Squares with multiple colors contain a number that’s used in the product for adjacent regions of each of those colors.  
• Remember: numbers can repeat within a shaded region if that doesn't violate the first rule. 

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)).