Saturday, March 26, 2011

Dr. Sudoku Prescribes: Borderlines

By Thomas Snyder
March 25, 2011 |
12:30 pm

Thomas Snyder (aka Dr. Sudoku) is a two-time World Sudoku Champion and five-time US Puzzle Champion, as well as the author of several books of puzzles. His puzzles are hand-crafted, with artistic themes, serving as a kind of ?cure for the common sudoku.? Each week he posts a new puzzle on his blog, The Art of Puzzles. This week Dr. Sudoku continues to experiment with a new kind of loop puzzle, with harder challenges than last time.

Last week I explored a simple loop variation that was (as I expected) received as a bit “easy”. One commenter noticed that the rules, which gave a strict count on unused loop segments, made the type essentially a slitherlink variant with fixed but unprinted numbers and I totally agree. I could not use the experimental Nikoli formula to make interesting puzzles because it is simply a bit too limiting. But the concept was inspiring which is why I played with its construction for awhile.

Having shown you the “simple” form, I now want to introduce my own variation called “Borderlines”. This is still a puzzle about irregular regions and loop constraints regarding the borders. However, the rules now requires you to either use a total length N, or to not use a total length N, around each region of size N and this increased flexibility leads to a whole new set of properties. There are a few logical “rules” to discover in the puzzles below, and they should certainly be harder than last week’s.

Rules: Draw a single closed loop that does not intersect itself using just the dotted lines of the grid. Each colored tile of area N must have either a total length of used dotted segments of exactly N or a total length of unused dotted segments of exactly N along its border.

Example: