Erasable Games Weblog

(Sudoku in words and pictures)

Extra Regions Sudoku

Extra Regions Sudoku

The idea for this Sudoku variant comes from the instruction booklet for the national Finals offered on March 23, 2008. While their example in the booklet doesn’t give any starting numbers, I thought that toorestrictive, so I do offer them. This is found on the World Sudoku Championship 2008.

In this age of the internet, everyone is (unnaturally) interested in everyone else’s opinion. You get it via Email (spam), Pop-up Windows, home page portals. So for those for whom answering surveys is an avocation, I offer the 1 question, universal question survey. To add to your convenience, the question is offered for your personal reflection, so you needn’t send it anywhere (especially here).

Last month, I noticed on the Usenet Newsgroup rec.puzzles, a stirring discussion about the question by Anthony Buckland, of:

Is the popularity of Sudoku dependent on computers?

Not for solution, but for creation. Can a new Sudoku for the newspaper each day reasonably be produced with nothing more than pen-and-paper technology? By, in the same way as crosswords and other puzzles, one person in the time that a newspaper (chain, if you like) fee would make worthwhile?

This may conform to a generational answer. Those who lived all their lives with computers may not be able to imagine life without them and underestimate human ingenuity. Those like me who fully embraced Computers starting in 1962, as an adult, know full well, computers are unnecessary for this endeavor. Many others, may consider this question a definite maybe.

As a simple example, it might take time to create a solved sudoku puzzle. But once done, a bit more time to create a set of starting numbers leading to one solution. Once you have this, you can create, using typesetting machinery, many sudoku puzzles from that one solution: Rotate the grid 90 degrees, Permute each component of vertical or horizontal blocks (e.g. Row 1 –> Row 3; Row 2 –> Row 1; Row 3 –> Row 2). Numbers can be mapped to other numbers for different puzzles.

In fact, of the 6,670,903,752,021,072,936,960 possible unique results that offer exactly one solution. The same puzzle looks totally different, when successively rotated 90 degrees, or by mirroring (reflection) or by relabeling the digits. When these effects are ignored, there are merely 5,472,730,538 essentially different Sudoku grids.

Questions That arise:

Can you trust a Sudoku that is created by hand? (Misprints happen even now)

How many puzzles can be generated per day, per week etc, if done only by hand?

Would there be as much (or more) starting number symmetry with hand puzzles?

Check out the 2008 World Sudoku Championship starting this week.

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