Month: May 2008

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Superscript Sudoku

Superscript Sudoku

Many Web-based Sudoku puzzle sites offer hints in the form of small sized superscripts (like exponents in Algebra). See my favorite site: Seattle Times Sudoku Page. These superscripts are also known as candidate numbers, which represent the remaining possibilities for values in a cell given the starting numbers (which are normal sized and ordinarily displayed).

It occurred to me that it would be very interesting to throw away the starting numbers and just deal with the superscript hints. Some people create these superscripts in all blank cells as a way to solve the puzzle anyway.

What I did is to initially clarify the proper values from the superscript cell entries to the best that I can determine. Then by looking at the blank cells, I noted that superscript values and totally blank cells contained mutually exclusive values. From that I could deduce the value that must be in a blank cell, based on those superscripts along its row, column and block.

It’s an unusual handicap that provides an enjoyable solution process. Solve on!

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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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Kanji Sudoku

Kanji Sudoku

I was watching the 1st Season, 1st Episode of the U.S. Television Series Heroes on DVD when I noticed a clock with Kanji Characters in a scene with Masi Oka (playing Hiro Nakamura). This led me to do this cartoon.

With non-english alphabets that do not share characters, I find it relatively easy to stare at each glyph and relate it to a sound or number and remember it. (My foreign language skills have otherwise languished.) The games Mah-Jong and Shogi have helped enormously to give me practice in this kind of character recognition.

There are some web sites that facilitate this practice:

I hope solving the puzzle in Kanji doesn’t slow you down too much.

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Reversi Sudoku

Reversi Sudoku

Earlier today, at my grandson Keegan’s 1st Birthday Party, I talked with a friend of mine (and another Keegan Grandparent) who sells books. Old books. He calls it: Lou Manrique — Antiquarian Bookseller. He talked about his recent passion for playing Reversi online with folks worldwide (but one at a time). Wikipedia goes into great detail about Reversi.

A long time back, I played the same game under the name Othello, something the Japanese trademarked back in the early 1970s. But in practice, Reversi and Othello are synonymous. Interestingly, There is a World Othello Federation.

Lou got me to thinking about how I could combine Reversi and Sudoku. Out of that comes this cartoon today. I imagine that you can solve the sudoku puzzle, but as you add a number to the board, you now also have to choose a black or white number. As you complete the puzzle, the board gets more fully filled in, perhaps by alternating black or white pieces.

Once the puzzle is solved, Reversi rules take effect.

A legal move in reversi is one which will complete linear envelopment at least one opponent’s disc and convert the disk(s) to your initial color. Play passes to your opponent if you have no legal moves. No legal moves for both players means the game ends and your territory extent is counted.

Now starting from the interior, it is necessary to flip linearly enveloped opposite colored numbers to your initial color (black). You alternate flipping to black, then to white, until there are no more flips possible. Then notice which color is more popular. It’s probably much better with two people playing.

To (re)freshen your skills playing Reversi, there is a computer Applet which you can play: See Reversi Java Applet By Thomas Wolf.

Consider solving this Sudoku Puzzle variant as bait for getting someone to help you finish the Reversi portion.

There is also a Reversi variation you can play in this! It’s called Reversed Reversi, where the goal is to minimize territory (i.e. lose). Just let your opponent know your objective, so that the game is more interesting.