Erasable Games Weblog

(Sudoku in words and pictures)

Archive for April, 2008

Domino Pairs Sudoku

Monday, April 28th, 2008

Domino Pairs Sudoku

The last cartoon that referred to Dominos and Sudoku occurred on March 30, 2007. At the time, I was more concerned with the number representation shown by the spots or “pips” than the tiles or “bones”.

So with this cartoon, I offer a variant using the tiles of a double nine set of Dominos.

A little analysis shows that a 9 by 9 Sudoku board permits a filled in arrangement of 40 tiles, keeping 1 cell uncovered. In this cartoon, I choose that cell to be the center cell, identified and covered by a circular single pip. For clarity, the starting tiles that are horizontal, have their border tinged in bright blue. Vertical tiles are shown in black.

Unfortunately, a double nine set of dominos contains 55 tiled pieces, of which 19 are inappropriate for Sudoku uniqueness rules (all tiles containing a blank and all the symmetric pairs). That leaves up to 36 unique tiles to place. This means there will be at least 4 tiles that are “cloned” in order to solve the Sudoku puzzle.

Fortunately, the tiles with pips are rotationally symmetric, unlike numbers printed on tiles, so they can fit into whateveer sudoku nook is required.

In keeping with the “solving rules” of this variant, place tiles or adjacent numbers two at a time. This is an unusual way of solving sudoku, especially at the beginning when you may be hard-pressed to find even a single number.

Perhaps you should invest in a double nine domino set as a solving aid and have a paper copy of the puzzle in progress to record your emerging solution, and place tile pairs only as they become available.

Sudoku XV

Sunday, April 20th, 2008

Sudoku XV

The 3rd World Sudoku Championship (with classic and variant puzzles) has been won by Thomas Snyder of the United States. In second place is Yuhei Kusui of Japan and Jakub Ondrousek of the Czech Republic who placed third. Mr. Snyder also won the Classic Sudoku Championship (no variants), followed by David McNeill of the United Kingdom in second place and Michael Ley of Germany in third place. Team competition results show the Czech Republic in first place, followed by Japan and Germany in 2nd and 3rd place, respectively.

One of the variants shown in the Instruction booklet (First Link in the Downloads Section, a PDF file) for this year’s contenders is known as Sudoku XV. The fewer numerical clues are offset by number pair relationships as sums of 5 or sums of 10. You may use the full force of sudoku analysis to fill in numbers and get the bonus of a neighboring pair value.

There seems to be few puzzle sources for this variant except in Competition instruction booklets. I hope this is temporary. It’s an interesting blend between a limited Kakuro and Sudoku.

Extra Regions Sudoku

Sunday, April 13th, 2008

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.

Cross Sums Sudoku

Monday, April 7th, 2008

Cross Sums Sudoku

So the question is: Does giving totals for all outer 3 cells (across and/or down) in selected 9×9 squares give the ability to solve a sudoku puzzle with a reduced collection of starting numbers? Because the interior (to the left of the 4th column and above the 4th row) has no space to specify their sums, I’ve chosen normal starting numbers instead.

The book by Xin-She Yang, Ph.D., called Cryptic Kakuro and Cross Sums Sudoku offers cross sums of all the 9×9 squares by creating wider detachments between them. There are no starting numbers as a result.

This puzzle also differs from traditional Kakuro Puzzles in that the entire 9×9 grid is used. In Kakuro, only a subset of the grid is used. See my cartoon on Kakuro last May 27, 2007.

Although I tried to offer all possible sums (combinations) of 3 unique single digits 1 through 9, there are too many to list. Trust in symmetry to help furnish the rest of them, if needed.

In other news, the 3rd Annual World Championship Sudoku Competition has just provided some downloadable materials for study and sample variations that (we and) the contestants may work on. Note that in the individual competition, Sudoku variants score double the points of Classical Sudoku puzzles where the expected solving time is the same.