August 25th, 2008 by arkay
There’s been a significant increase in traffic to this blog ever since I posted the Numbrix puzzle variant at the end of July. For that, I thank you all for visiting.
This week, Barnes and Noble displayed a book by Dr. Gyora Benedek, called Hidato (A Hebrew word meaning: My Puzzle). Dr. Benedek writes an excellent (short) autobiography. The book itself contains variously sized and shaped grids including nonsquare (and nonquadrilateral) ones. Some webbased 10 x 10 grids have an interesting characteristic in that the middle 4 cells are darkened, indicating that they are not in play, leaving 96 cells to the playing area.
Typically, you’ll be connecting sequence segments based on the starting numbers. Luckily, the connectedness of the overall sequence requires that local neighborhoods of numbers be near in value. What provides a challenge is that It is possible that multiple such sequences may be intermixed.
On the negative side, there’s no facility for saving the current state of the puzzle (without printing it) and when you print the puzzle out, it does not let you return to the puzzle to continue with it.
Have a good time with this variant. This is just the beginning for it.
Tagged with Hidato, Minesweeper, Numbrix, Sudoku Puzzles, Sudoku Variants, Varieties of Sudoku, Web Comics  1 Comment »
August 11th, 2008 by arkay
A while back, I created a Cartoon called Double Sudoku. In that variant, there were 2 totally separate Sudoku Puzzles embedded in a single Sudoku Grid with all split cells.
The current cartoon is reminiscent of that one, but has N1 starting numbers that are the same for both puzzles. (Double Sudoku had all different starting numbers for each puzzle.)
In researching where this variant may exist on the internet, I came across a site called SuBundle.com, by Dr. Chen, which has generalized this concept even further. Provided are puzzles with as many as 256 possible puzzles generated from multiple “Key Cells” in a single grid.
Normally, a “Key Cell” either contains a single digit M, which signifies that there are that (M) many puzzles bundled together (and you must figure out which digits lead to a solution) or the “Key Cell” contains multiple digits, which means that each of those digits leads to a different Sudoku puzzle.
Truly, this is a “Green” website for Sudoku Puzzles, where the number of Sudoku Grids is severely conserved. His site even offers multiple blank Sudoku grids that may be printed from a pdf or png formatted file.
I’ve provided tips for solving the above puzzle in the single grid by splitting blank cells in two parts. Of course, you can write each puzzle out on paper or duplicate electronically and solve each normally (and one after another).
I hope you enjoy solving this example of Sudoku puzzle cousins twice removed!
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August 4th, 2008 by arkay
This cartoon has at its root, a cartoon from 3/4/2007, called Linear Sudoku. For those that wish to describe a Sudoku puzzle to others, particularly by Email, the best way is to create either an 81 character text string or a 9 strings of size 9, where the dot represents the blank cell in both cases.
The site: Sudoku @ Paulspages permits the selection of a Sudoku puzzle, be it random, nonsymmetric or from a gallery of puzzles and from that point, it is possible to export it as a text file as shown to the right of the Board in this Cartoon.
There are several benefits for this format, not the least of which is communicating with another puzzler to verify a difficulty or a solution. For those who are visually impaired, they can employ a software program that converts text to speech, thereby permitting the person to hear what the puzzle elements are, so that they can be solved mentally, or transcribed to a braillewriter for reference.
Now that text messaging is becoming most popular, these text strings can convey a puzzle in a minimum of words. This can be useful in timed competitions, where the winning solution is “texted” over to the contest judges for least time and solution correctness. See, for example:
Sudoku Text Challenge sponsored by the TimesOnline and retrieved June 17, 2008.
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July 28th, 2008 by arkay
On July 13, 2008, Marilyn Vos Savant, in her column Ask Marilyn, (which is syndicated through Parade Magazine) introduced a number puzzle which helps focus the mind. It’s called Numbrix^{TM}.
According to Michael Keller, of Solitaire Laboratory, who commented in the newsgroup rec.puzzles on July 22, 2008:
This puzzle dates back at least to 1981, when Steve Wilson (who I think invented it) published some puzzles in Games Magazine (July/August 1981, page 38). Steve’s puzzles are much harder and more interesting than Marilyn’s pathetic examples.
The puzzle in its present incarnation seems easy to those with much numerical puzzle experience, but can be challenging to those people with number anxiety and/or with interruptdriven lives.
Although Marilyn’s puzzles are on 7×7 and 8×8 grids, there’s no reason why a 9×9 grid can’t be fully used. I restrained myself from making it harder by eliminating selected edge numbers, but that could be done by you, when copying the initial puzzle.
Stay on the path and be enlightened (or at least delighted), once you finish the puzzle.
Tagged with Math, Numbrix, Sudoku Variants, Varieties of Sudoku, Web Comics  4 Comments »
July 20th, 2008 by arkay
I received a wonderful (analog) watch from my niece. It was a Square Root Watch! As a math instructor this made me smile and be pleased with my niece for thinking of me.
The watch is really a lowtech encryption of time, especially for those whose instant reaction to any mathrelated symbol is anxiety. Look at: signals.com if you’d like to acquire a watch like this and also impress your friends. It’s has made everyone laugh who I have showed it to. Of course, the watch wearer may have been the source of amusement. 🙂 hah!
As a result, I adapted this concept to Sudoku puzzling. The result is the cartoon for today. Enjoy the puzzle but don’t be absurd.
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July 7th, 2008 by arkay
My wife pointed out that in no way are solving the puzzle and making a tune in a cause and effect relationship. In the interest of clarity, what I really mean is for you to solve the puzzle and then sing, whistle, hum, play, and/or listen to any tune of your choice, composed by you or anyone else. This way, all can take part.
As I look at these musical symbols, I am aware that these look perfectly natural to me, since I learned to read piano music at the age of 5. I’m sure there are those for whom these symbols are mostly strange.
Music notation and symbols have long term strategic importance for preserving musical compositions for future generations. It is a true encoding. Various media containing musical sounds: Cylinders of the early 20th century, 78 RPM phonograph records of the 1920s1950s, 45 RPM records (1950s), 33.3 RPM long playing records (19501980s), Audio Tape (19601980s), and CDs (1980now), MP3s (2000now) may appear to be lasting, but just remember that all of them require a device to play the media. If the device is not available, the physical media become merely fashion statements and the electronic media become indecipherable. Musical notation on sheet music persists!
Enjoy your summer, now that it is finally here! Muse on the puzzle.
Tagged with Music, Varieties of Sudoku, Web Comics  1 Comment »
June 29th, 2008 by arkay
Today’s puzzle variant comes from the 2008 Sudoku World Competition Instruction booklet. I’ve renamed it Even Sum Sudoku for clarity. About a year ago, I published a cartoon called Odd Sudoku, where either Odd or Even contiguous Cells of at least size 2 were offered. This is not like that.
I’ve eliminated some starting numbers from the original puzzle and identified the cells in yellow as pairs with values summing to an even result.
One question that occurs to me is: what is the probability of having Even Sum Pairs for all the arrangements of this puzzle? Obviously, there are at least 8 Even Sum Pairs that have already been earmarked. From previous calculations (Domino Sudoku Cartoon), excluding the center cell, there are 40 pairs of contiguous cells in an arrangement (and there are 2**4 = 16 pair arrangements since:
 In Row 1, columns 1 and 2 [A = Across] or the other starting in Column 1, Rows 1. 2 [D = Down]
 In Row 2, columns 2, 3 [A] or Column 2, Rows 2, 3 [D]
 In Row 3, columns 3, 4 [A] or Column 3, Rows 3, 4 [D]
 In Row 4, columns 4, 5 [A] or Column 4, Rows 4, 5 [D]
Since each of these can be selected independently, there are 2*2*2*2 = 16 arrangements.
For any arrangement, how many are Even Pairs are there? It turns out, once you’ve solved the puzzle, you can count:
Across [A] 

Down [D] 
Odd: 8 Even: 8 

Odd: 10 Even: 6 
Odd: 9 Even: 3 

Odd: 7 Even: 5 
Odd: 3 Even: 5 

Odd: 5 Even: 3 
Odd: 3 Even: 1 

Odd: 3 Even: 1 
Totals: 

Odd: 23 Even: 17 

Odd: 25 Even: 15 
Arrangement 
No. 
Odd 
Even 
AAAA 
1 
23 
17 
DDDD 
2 
25 
15 
ADAA 
3 
21 
19 
AADA 
4 
25 
15 
AAAD 
5 
23 
17 
DAAA 
6 
25 
15 
ADDA 
7 
23 
17 
ADAD 
8 
21 
19 
AADD 
9 
25 
15 
DDAA 
10 
23 
17 
DADA 
11 
27 
13 
DAAD 
12 
25 
15 
ADDD 
13 
23 
17 
DADD 
14 
27 
13 
DDAD 
15 
23 
17 
DDDA 
16 
25 
15 
Frequency 
Odd 

Even 
2 
21 

19 
6 
23 

17 
6 
25 

15 
2 
27 

13 
P(Even = 19) = .125
P(Even = 17) = .375
P(Even = 15) = .375
P(Even = 13) = .125
A nice discrete, symmetric binomial distribution! Enjoy getting even.
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June 22nd, 2008 by arkay
After the rain or flooding, there will be worms that surface to find a new nesting place.
Where I live, rain has been a constant companion since last October. Other parts of the world (Myanmar, China, near the Mississippi River) have significantly more extreme weather and climate. My hat is off to them abiding under such conditions. I am sad for those who have lost loved ones, pets, possessions and stability they worked so hard for to flooding.
Laura Taalman’s Brainfreeze Puzzle Math Variants contains a variation called Worm Sudoku (in green type on that page). I have varied it further to not offer sequence direction nor offer two cell sequences nor different color (nor turning) worms.
Other sites with a worm variation include a German site (sachsentext.de) containing a huge number of variant Sudoku puzzles: Sudoku X Worms and Threesixty360.wordpress.com which heralds the upcoming Mathfest (August) 2008
No doubt, the above puzzle is fairly easy to solve compared to those on Brainfreezepuzzles.com. My wife has insisted that I offer more easily solved puzzle examples, since the variations are confounding enough. So here it is.
If this puzzle makes you squeamish, consider the real thing: Sudoku Worm!
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June 9th, 2008 by arkay
Because of the natural correspondence of sequential alphabet lists of letters to positive integers, many nonenglish alphabets have a strong link to number sequences. The Hellenic (Greek) letters offer a numeric code that can be used to vary Sudoku puzzles.
In reviewing the connotations of this alphabet and its relation to Mathematics (and Statistics), I discovered several interesting sites:
Since I used the Font Face MMa Greek Bold, it automatically translated the number 6 into a righttoleft flipped 3. The original Digamma was more like an F or f. Go figure (so to speak).
This puzzle is considered more than medium difficulty, but if you have become facile in manipulating 9 symbols, the essence of the Sudoku logic should produce a solution sooner than later.
“Wonder is the beginning of wisdom.” — Greek Proverb
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June 1st, 2008 by arkay
In reviewing the accumulating collection of Sudoku variants, I noticed that I never offered the “straightforward” mapping of letters for the digits 1 through 9. I hereby remedy this oversight with this cartoon.
This puzzle is also the outgrowth of a “commission” for me to produce a Sudoku puzzle with special letters spelling out a company name and project acronym. This puzzle is to be used as something to do while listening to how wonderful the future of specific software will be. As always, any feature of the future indicates what is not a feature of the present software. (Once upon a time, this too was future shock and awe.)
This puzzle is rated hard, especially using letters, if you are not used to them. Good luck!
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