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Inverse Sudoku

Inverse Sudoku

Like most interesting games, when turning them around by redefining what loses is now what wins, a fascinating variant can be played. For example, in Chess, if the object is to now be the first player to lose all pieces except the king, and a capture is forced if it is available to be played, this yeilds a variant, called Losing Chess that even novice players can excel at.

Another game is called Losing Checkers where you play Checkers according to normal rules (forced to capture if the opportunity arises) but the Loser wins.

In this spirit, I thaought about what it might mean for Sudoku puzzle solving. Since there are so many ways you can fail to solve a puzzle, this didn’t seem to challenging 🙂

In this Cartoon variant, We start with a Sudoku solved puzzle and proceed to erase numbers until we have an incomplete or starting puzzle (depending on when you stop erasing). Then try to solve the puzzle that is presented.

If you don’t erase enough numbers, the puzzle may be easily solved. If you erase just enough numbers, (in this case 53 of them), you may either have a uniquely solvable puzzle with a single solution or you may have one with more than one solution. If you keep removing more than 53 numbers (in this case), your ultimate solution may have multiple answers. This means that your starting numbers are “ambiguous”.

There are many programmatic aids in solving sudoku puzzles on the internet, both web based and downloadable applications. One category are Sudoku Puzzle Generators where they produce the starting numbers and you solve. There are also Sudoku Solver Sites, many of which have user interfaces so that *their* puzzle may be solved by you online.

The trick is to find Sudoku Solvers where you get to input the starting numbers. Some sites I found offer:

(1) Excel based Sudoku all in one Generator and Solver by Hari Kumar

(2) Excel based Sudoku-xls Generator, Workpad and Solver by Peter Mladek

(3) AT&T Research Command line: A 9 x 9 Sudoku Solver And Generator And Starting Number analysis

(4) GNUDoQ 0.94 Sudoku Solver

(5) David Ireland’s Number Sudoku Solver (Excel Based)

Happy Erasing!

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More 2007 World Sudoku Championship And More Color Sudoku

I’m slowing catching up on the news: On February 3, 2007, The World Puzzle Championship announced the U.S. Sudoku Team Members for the 2007 World Sudoku Championship.
They are:

  • Nick Baxter, Captain and Members:
  • Grayson Holmes (placed 50th in 1st World Sudoku Championship March 2006),
  • Wei-Hwa Huang (placed 2nd),
  • Jonathan Rivet,
  • Jim Schneider (placed 28th),
  • Thomas Snyder (placed 1st),
  • Jason Zuffranieri

In the livejournal community called worldpuzzle, there are many details about the upcoming World Championship including instructions (a downloadable pdf file).

There are new kinds of puzzles depicted, which are different from those in 2006. I especially like the puzzle called Paint It Black, which is a blend of a Sudoku Puzzle and a Paint By Numbers Puzzle.

Two Color Sudoku Sites that I noticed are a Color Sudoku Journal Article and a Color Sudoku Solver in MS Excel.

The Journal of Chemical Education is publishing an article called “Chemistry of Art and Color Sudoku Puzzles” by Michael J. Welsh of the Department of Science and Mathematics, Columbia College Chicago, Chicago, IL 60605

The abstract describes what may be a fascinating connection between chemistry and color. Unfortunately a paid subscription to the Journal ($45 for US Individual) is required for both the full text of the article and the 3 puzzles and solutions file shown in the article.

Quite free is the Color Sudoku Solver via Excel Spreadsheet by Erkki Hartikainen: downloadable xls file. This spreadsheet solver permits you to map the digits and colors in either direction.

One particularly handy feature is the ability to modify colors depending on your own eyes’ ability to distinguish contrasting colors. The color solver is based on a number Sudoku solver by David Ireland.

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Usenet And Sudoku Susser

Before the Web was in evidence in 1991 (see history), there was Usenet News, which started in 1979. It grew to consist of myriad newsgroups, even in the 1980s. Computer servers, as a public service, dedicated some of their storage to a rolling database of hundreds and later thousands of newsgroups containing messages going back several days to several weeks before the oldest messages were sloughed off in favor of the latest messages. The mechanism used was a form of uucp (Unix to Unix Copy) which stored and forwarded the message base from one Computer system to another.

Within Usenet, there existed binary newsgroups that allowed freeware, shareware, updates to existing applications that were regularly made available. See a short history of Usenet.

A while back, I was reading the newsgroup: rec.puzzles, a very large online discussion group, I searched for the subset of articles that involved Sudoku (using the Unison Newsreader on Mac OSX 10.3.9). From these (over a thousand messages), There was a message relating to the Multi-Operating System product (Freeware) called Sudoku Susser by Robert Woodhead.

He is the author of Two Sudoku books: Sudoku To Go! and Brainiac’s Sudoku Puzzle Book. The first is an adult puzzle book and the second one is more for kids or novice learners.

I’m impressed with Sudoku Susser. It is interesting because of its user interface support for various intermediate and advanced solving techniques. You can also drag and drop puzzles to solve from the Web or as files and the software will attempt to read it in.

Since the author of the books is the author of the software, Supplying the ISBN number to either book will automatically load all the puzzles in that book! The type of freeware requested is called tipware. I.e., pay what you can, if you want. I like this software’s user interface even better than that of the Seattle Times Sudoku Puzzle (which they offer via content.uclick.com), which is my favorite online web interface.

I solved the initial easy puzzle to test how the default interface worked. Every move you make is tracked. All possibilities (variable sized depending on how many) are specified in the non-starting number squares, making the puzzle a fast pleasure to solve. When highlighting a square, the non-possibilities are also shown to verify your candidate value. There are options for toggling “annoying” sound effects and an “embarrassing” timer.