Erasable Games Weblog

(Sudoku in words and pictures)

Entries tagged with 'Sudoku Variants'

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.

Mirror Sudoku

Sunday, March 30th, 2008

Mirror Sudoku

There seem to be three kinds of mirroring: What you see in a mirror, mimicry and instant object replication. The first depends on symmetry, the second depends on synchronicity and the third on identity. Andrew Carson of Dungeon7Sciences discusses what a mirror image is about and why the mirror doesn’t show us upside down as well.

In psychological or theatrical terms, mirroring (mimicry) is concurrently copying what someone else is doing (perhaps while communicating with them). Group synchronized dancing (or swimming) are good examples of this. It is called satire when the mimicry is delayed.

In Computer terms, a mirror is an exact copy of data of some extent of storage. On the Web, mirrors contain repositories of desired software or replicated data, useful when there is a surge in demand for a particular article, picture, software program or datum.

There is a description of Mirror Sudoku which requires that the Sudoku puzzle starting number placements be symmetrical horizontally and/or vertically. This puzzle with its starting number positions conforms to horizontal and vertical symmetries.

Remember to draw the numbers slowly and precisely. It’s an alternate universe you’re trying for.

Fillomino On Sudoku

Sunday, March 23rd, 2008

Fillomino On Sudoku

Nikoli invented this puzzle in 2001. Once called Allied Occupation, Fillomino is a merger of the words Filled and Polyomino. A Polyomino describes the shapes assumed of a varying number of multiple cells, that have at least one side touching another cell.

Wikipedia describes this as a logic puzzle and gives more elaborate rules, particularly about the possibility that 2 or more given numbers could belong to the same pentomino. Solution methods are also offered.

As this is a fairly popular puzzle in its own right, there are a variety of Websites that offer Fillomino:

  • Puzzle Club a British Site offers Many Math, Number, Logic, and Word Puzzles in addition to Fillomino. Registration is 10 Pounds/Year
  • Vegard Hanssen’s Fillomino Puzzles, which has more than 16,000 Puzzles in its database. Mr. Hanssen is a perl programming language afficionado, See his perl scripts for generating his name(s).
  • provides 8x8s, 12×12 and 16×16 size grids for their daily Fillomino puzzles.
  • Simon Tatham has a similarly named puzzle called Filling on his website.
  • Finally, has an interesting discussion about Fillomino Skyscrapers which is a mashup of Fillomino and what I called buildings. The numbers on the outside are clues to how many “buildings” can be viewed from that location. Higher valued numbers block lower valued numbers, but offer interesting clues about the composition of the row or column. See my Sudoku Buildings Cartoon posted last July 15, 2007.

Get your fill of Fillomino! (but take your time.)

Signal Pennant Sudoku

Sunday, March 16th, 2008

Signal Pennant Sudoku

The use of flags and pennants as communications has intrigued me. According to the Sea Flags web site, Athenian (Greek) ships were first known to signal each other with brightly colored flags. Time passed and Navies of various European countries began to devise more sophisticated communication using semaphores and flaghoists after 1750.

The current situation is depicted in the International Code of Signals and in particular, pennants representing the digits one through nine are shown in the cartoon.

It’s an easy leap to create a sudoku puzzle using these pennants as stand-ins for the normal digits. You may do this puzzle calmly and in a room that has been becalmed as well.

Time Change Sudoku

Sunday, March 9th, 2008

Time Change Sudoku

In most of the United States (But not Arizona nor Hawaii), Daylight Saving Time began early this morning, March 9. I find out how many clocks I’m governed by when I do this twice-yearly ritual. Occasionally, the clocks I missed last fall are telling accurate time now and they stay unperturbed.

I found an interesting Web Site called describing Daylight Saving Time and which uses a kind of a mind-map (that they call clouds or nodes) to display information, in lieu of powerpoint-like slides. For this, you must let go of outlines and hierarchy.

Wikipedia has a colored map of use and abstinence of DST (or Summer Time) Worldwide.

To honor the induced chaos of time changes, I’ve created a Sudoku Puzzle which uses analog clock faces. Take your time.

Usually at this time of year, the Yearly Sudoku World Championship announces itself. Based on a cursory web search, The 2008 Sudoku World Championship will be held on April 14-17, 2008 in Goa, India on the West Coast in the Konkan region and bordering the Arabian Sea.

Registration apparently started March 8, 2008. This year publicity is currently sparse, so much information emanates from a Technical Blog called Revisit it during the next month, for further details.

Scrabulous On Sudoku

Monday, March 3rd, 2008

Scrabulous On Sudoku

Based on the March 2, 2008 New York Times Article about the dilemmas posed by Scrabulous™, an online game invented by Rajat and Jayant Agarwalla, from Kolkata, India, this cartoon was born.

The online game appears to be an intimate embrace of Scrabble™, currently physically sold and distributed by Hasbro, Inc. and Mattel Inc., who together divide up the World Rights to sell the game.

As is becoming clearer in the 21st century, having an online version stimulates sales of physical (original) versions. By squelching the online versions, these companies risk severe sales reductions due to bad publicity and a collective vow to boycott those company products. By not squelching the online versions, the companies must adapt (like the music and movie industries are [not] doing) or go out of business anyway. Choose wisely.

I thought it would be amusing to mashup Sudoku with Scrabulous. You can play it with either game goal in mind, but pursuing both will no doubt mentally bifurcate you, which is a serious condition, sometimes leading to split personalities.

Eye Chart Sudoku

Monday, February 25th, 2008

Eye Chart Sudoku

Have you ever been to the Eye Doctor (Optician, Opthalmic Dispenser) and got tested for your visual acuity and thought: “This test is too easy!” ? I have. The result is this cartoon. I heartily recommend it to all who have to get their vision checked. Try to talk your doctor into using this chart rather than his. You may both be surprised at the results. Consider it a Vision Quest.