Elasticity

Title: Elasticity

Rating: 3/5

After last week's mod 9 sum, this week is a mod 9 product.

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 (mod 9).   
• 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.  

Modular Lightning

Title: Modular Lightning

Rating: 2/5

In the first of three puzzles of this type, modular arithmetic plays an important rule.  Here, all the sums are given mod 9.

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 (mod 9).   
• 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. 

Missouri Mule

Title: Missouri Mule

Rating: 2/5

The titular drink is destined to provide a kick.  Created by Harry Truman, it's a combination of bourbon, Applejack, lemon juice, Campari, and Cointreau. 


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.

Discontinuity

Title: Discontinuity

Rating: 1/5

The title comes from the overlapping regions in the center square.  Note that the number in the center is part of both the horizontal and the vertical regions through that square.

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.