Baby's Room

Title: Baby's Room

Rating: 2/5

We're back to a sum puzzle.  At this stage of creating puzzles, colors were chosen from a random starting point and then averaging some RGB values for the remaining colors.  As the last post stated, color generation became more sophisticated/intentional for the mix puzzles.

As a reminder, 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.  
• Several initial clues have been given in larger font.
• Remember: numbers can repeat within a shaded region if that doesn't violate the first rule.

Horse's Neck

Title: Horse's Neck

Rating: 1/5

The final variety that comprises a big chunk of these puzzles mixes the sum and product puzzles.  Some regions require a given sum be achieved, while others require a given product.  The notation + and * before the number indicate which operation is relevant for a given region.  

You may also notice as more puzzles are posted that the titles for these "mix" puzzles have more meaning than those for sum or product puzzles.  Names of these puzzles (and the color schemes) were inspired by mixed drinks.  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.

Color Blind

Title: Color Blind

Rating: 1/5

This is the first puzzle of the sort I'd call a "product" puzzle.  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.

Elements

Title: Elements

Rating: 2/5

The first puzzle is one that I'd call a "sum" puzzle.  Here are 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.  
• Several initial clues have been given in larger font.
• Remember: numbers can repeat within a shaded region if that doesn't violate the first rule.

How it began

Many moons ago, Sudoku became popular in the U.S., and as a math nerd, I started solving the puzzles.  Soon, though, I required something besides the standard puzzle arrangement to keep me interested.  Luckily, Brainfreeze Puzzles came along at that point with some variants.

They had two mathematical variants that piqued my curiosity.  One of their variants was with "worms," where extra conditions occurred through regions that didn't have to stay in one column or one row.  They also produced variations with sums and products in certain regions.  The puzzles maintained a symmetry in the shapes of the regions and in placement of initial clues, and I thought that produced some cool visuals through puzzles.  It also led me to wonder about a couple of things:

• What would happen if one kept the usual Sudoku restrictions of one of each character per row and column but dropped the restriction of the 3X3 subgrids?  And even more than that, what if there could be repeated characters in the worms, as long as the rule against multiple characters per row or column wasn't violated?
• And these worms....they're friendly, right?  So what if two (or more) worms decide to share a square in the 9X9 board? 

I started to dabble and produced a few puzzles for a Problem of the Month series (specifically, April 2011, October 2011, March 2012, and February 2013).  But that dabbling was just the tip of the iceberg.  Over the last 2 1/2 years, I created a series of 100-ish puzzles, and it's time for someone besides me (hopefully) to work on them.  I'm a fan of the symmetry, so if you rotate the puzzles, you'll see the same shapes (perhaps with "rotated" colors, perhaps not).  Some of the puzzles involve sums, some products, some both.  A few of them are one-off variants created just to shake things up.  I've given what I think is an accurate rating to each of the puzzles, but I've been told that my judgment might err toward the underestimate.  Any feedback on how you'd rate the puzzle would be appreciated.

I plan to post a new puzzle about once a week.  Oh, and one more thing: I don't plan to publish solutions.  As certain spouses of time lords would say, "Spoilers..."

Enjoy.