I Want to Believe

Title: I Want to Believe

Rating: 3/5

Sometimes an idea takes hold for whether a certain design is possible.  I wanted to pay homage in my own small way to The X-Files, a show I adore.

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. 

Windmill

Title: Windmill

Rating: 3/5

As happened in a previous puzzle, this sum puzzle contains regions that overlap each other (instead of just abutting each other).  May your pursuits to solve this one not be quixotic.

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.
• Cells at the following positions belong to the regions that go horizontally and vertically through that cell: (2,2), (2,8), (8,2), (8,8).  The (light purple) color of these cells is the RGB-average of the colors from the horizontal and vertical regions that intersect there. 
• Remember: numbers can repeat within a shaded region if that doesn't violate the first rule.

Sea Breeze

Title: Sea Breeze

Rating: 3/5

It's starting to feel like winter, but perhaps this drink (a combination of vodka, cranberry juice, and grapefruit juice on the rocks) will bring back memories of warmer days.

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.

Rotation

Title: Rotation

Rating: 2/5

While all of these puzzles have rotational symmetry, this week's product puzzles strives to highlight that symmetry as clearly as possible.

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. 

Drip

Title: Drip

Rating: 3/5

A medium difficulty puzzle for a medium kind of December day.

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.

Amends

Title: Amends

Rating: 1/5

If the first of these was challenging, this second of the four "pentoku" puzzles I created should engender some good will.  It's one of the easiest puzzles I've created.

The official rules:

• The digits 1, 2, 3, 4, and 5 appear in the above puzzle.
• Each shaded region contains exactly one of each of the digits 1 through 5.
• No row or column can contain more than two appearances of any of the digits 1, 2, 3, 4, 5.
• Squares with multiple colors contain a number that’s used in both of the associated adjacent regions.

Tom Collins

Title: Tom Collins

Rating: 3/5

A classic drink headlines this week's mix puzzle.  Typical ingredients are gin, lemon juice, and sugar syrup, with a maraschino cherry as garnish.

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.

Central Office

Title: Central Office

Rating: 2/5

This week's product puzzle was modeled to more clearly exhibit the symmetry of construction.  Each of these puzzles has not just 180 degree symmetry, but a 90 degree symmetry, with colors consistently shifting as the puzzle rotates.

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. 

UFO

Title: UFO

Rating: 3/5

Don't be tempted to look at the sky.  Keep your eyes on the puzzle.

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.

Zurracapote

Title: Zurracapote

Rating: 3/5

This is a drink I hadn't heard of before I started creating mix puzzles.  This Spanish drink is made with red wine, fruits (in the case of the puzzle colors, peaches and lemon), cinnamon, and sugar.

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.

Storm

Title: Storm

Rating: 3/5

The weather's been rainy where I live for much of the last week, so this product puzzle will fit nicely.  The most challenging part of it involves the regions moving between more than two rows or columns.

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. 

Appreciation

Title: Appreciation

Rating: 2/5

In the continued vein of how things get named, I'm hoping you'll be able to cheer about the name for this one.  There are a few areas to be careful of, though.  Make sure to check out the rules 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.
• Cells at the following positions belong to the regions that go horizontally and vertically through that cell: (2,2), (2,8), (8,2), (8,8), (4,4), (4,6), (6,4), (6,6).  The (light purple) color of these cells is the RGB-average of the colors from the horizontal and vertical regions that intersect there. 
• Remember: numbers can repeat within a shaded region if that doesn't violate the first rule.

Bronx

Title: Bronx

Rating: 3/5

Typically made with gin, sweet red vermouth, dry vermouth, and orange juice, the Bronx has unclear origins dating before Prohibition. 

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.

Prorus

Title: Prorus

Rating: 3/5

Not your typical product puzzle this week.  The board is what I call a "toral board," so named because the board is meant to be viewed not as a big square, but as what's called a fundamental region.  In this case, imagine folding the sides of the square together to get a cylinder.  Then fold the ends of the cylinder together, and you get what's called a torus (a donut, if you will).  Those associations (between left and right, between top and bottom, and, hence, between all corners) are reflected in the rules below.

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. 
• The board is a “toral board,” that is, cells at the end of one row are considered adjacent to those at the beginning of the same row; cells at the end of one column are considered adjacent to those at the beginning of the same column, and all corner cells are considered adjacent.

A Four Color Problem

Title: A Four Color Problem (original)

Rating: 4/5

On the last sum puzzle, I had no inspiration for the title.  This week's puzzle is the first sum puzzle I created.  The second was published in MAA Focus; so consider this a two-for-one week.

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.

Papa Doble

Title: Papa Doble

Rating: 2/5

Also known as the Hemingway Daiquiri, this is made with white rum, the juice of limes and grapefruit, and some maraschino liqueur. 

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.

Churn

Title: Churn

Rating: 2/5

Only a little bit of agitation in this product puzzle, unlike the last one.

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.

Pending

Title: Pending

Rating: 3/5

Sometimes the puzzle just doesn't come out looking like anything to me.  As one of the few times that's happened, this sum puzzle got an generic title.

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.

Paradise

Title: Paradise

Rating: 2/5

The regular semester has started again.  In celebration of that, enjoy this apéritif, made from gin, apricot brandy, and orange juice.  It's then traditionally shaken over ice.  

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.

Stitch in Time

Title: Stitch in Time

Rating: 4/5

One of the harder product puzzles I've created, in part because of the larger products in the puzzle.  Good luck.

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.

Traffic

Title: Traffic

Rating: 1/5

This is an extremely congested puzzle, but it's not as difficult to navigate as it might seem.

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.

Bloody Mary

Title: Bloody Mary

Rating: 2/5

Enjoy this week's classic cocktail, a mix of tomato juice, vodka, and lemon juice, garnished by a celery stalk.

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.

Everything is Awesome

Title: Everything is Awesome

Rating: 3/5

This week offers another product puzzle whose title is inspired by blocks.

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.

Candy Center

Title: Candy Center

Rating: 4/5

 

One of the earliest puzzles of any type that I created, this happens also be one of the hardest.  Enjoy the treat.

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.

Five By

Title: Five By

Rating: 3/5

For a change of pace, here's an alternate puzzle.  Brainfreeze Puzzles recently released a book with 10 X 10 puzzles with pentomino blocks.  Having seen test runs of such puzzles a couple of years prior to that, I decided to see what that style of puzzle would look like with overlapping regions in a standard 9 X 9 board.  I created four such puzzles; this is the first.

The official rules:

• The digits 1, 2, 3, 4, and 5 appear in the above puzzle.
• Each shaded region contains exactly one of each of the digits 1 through 5.
• No row or column can contain more than two appearances of any of the digits 1, 2, 3, 4, 5.
• Squares with multiple colors contain a number that’s used in both of the associated adjacent regions.