Erasable Games Weblog

(Sudoku in words and pictures)

Archive for June, 2008

Even Sum Sudoku

Sunday, June 29th, 2008

Even Sum Sudoku

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.

Wormy Sudoku

Sunday, June 22nd, 2008

Wormy Sudoku

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!

Hellenic Sudoku

Monday, June 9th, 2008

Hellenic Sudoku

Because of the natural correspondence of sequential alphabet lists of letters to positive integers, many non-english 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 right-to-left 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

9 Letter Sudoku

Sunday, June 1st, 2008

9 Letter Sudoku

In reviewing the accumulating collection of Sudoku variants, I noticed that I never offered the “straight-forward” 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!