Sudoku: Is It Really Just a Game?
Satenig Ghiulezian
5/7/2013
Writing 340
Portfolio Paper #1
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Biography: Satenig Ghiulezian is junior majoring in mechanical engineering at the
University of Southern California. When she graduates she hopes to become a Disney Imagineer.
When she’s not studying, Satenig loves to spend her free time reading and solving Sudoku
puzzle variants.
Abstract: In the mid-2000’s, Sudoku became an extremely popular game. It seemed that
an ancient Japanese puzzle had just been reincarnated. Sudoku’s origins however are rooted far
from Japan. Besides being an entertaining puzzle for many, Sudoku has many interesting
applications in the scientific world.
Contrary to popular belief, Sudoku did not originate in Japan. In fact, the connection with
Japan ends with the name Sudoku. According to Will Shortz, the world’s only academically
accredited puzzle master, the credit for the first ever Sudoku puzzle belongs to a retired architect,
Howard Garns, who did not live long enough to witness the puzzle become a worldwide
craze[1]. The first Sudoku puzzle appeared to the public in 1979 in an issue of a puzzle
magazine, Dell, under the name “Number Place.” From there, the puzzle spread to Japan where a
magazine dubbed it Sudoku a rough translation of the English title, and subsequently
trademarked the name. The term Sudoku is an abbreviation of the Japanese phrase, Suuji wa
dokusin ni kairu, meaning “the numbers must occur once only” [1].
Sudoku became a world-wide phenomenon, similar to the craze of the Rubik’s cube in
the 1980’s, in 2005 when retired lawyer Wayne Gould created an automated Sudoku-generating
algorithm. Sudoku’s roots, however, date back all the way to magic squares from the Middle
Ages. Magic squares are square grids of n numbers or letters arranged in such a way that all the
numbers add up to a ‘magic number’ or all the letters spell a ‘magic word’. The simple
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configuration was viewed as “occult”, explaining the reason for it to be called magic, and was
actually taboo in the über-religious 15th century. [2]
Renowned mathematician, Leonhard Euler, who has countless theorems and constants to
his name, fascinated with magic squares, explored different configurations of them [2]. The Latin
Square, so called because Euler originally used Latin letters in his puzzles, is a matrix of size
nxn, such that no number from 1-n is repeated in any row or column. Figure 1 illustrates a
completely filled in Latin Square of order 9, ie. n=9.
Figure 1: A Latin Square of Order 9
Euler’s main interest was figuring out how many different configurations of Latin Squares
existed for a given n. Other than that, Euler found the Latin Square nothing more than a game,
even though he used the proof of different configurations to solve problems like the crossing the
seven bridges of Königsberg in present day Russia in a single path.
The use of numbers is completely arbitrary; any combination of unique symbols is
adequate. A Sudoku puzzle is a Latin square with an extra constrain: no number should appear
twice in an individual grid. Just like every square is a rectangle, every Sudoku puzzle is a Latin
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square. Similarly, not every Latin square can be called a Sudoku puzzle, just like every rectangle
cannot necessarily be called a square. An example of a completely filled Sudoku puzzle is shown
in figure 2.
Figure 1 A completed Sudoku grid
The puzzle, simple, yet enjoyable for the novice and veteran alike, poses many interesting
numerical questions. In the case of Latin squares, for each different n, there is a limit on how
many unique grids can be built. Obviously, the same applies to Sudoku puzzles. The number of
possible unique Sudoku combinations in a traditional 9 x 9 configuration is much smaller than
the same configuration for Latin square, because of the added restraints. Sudoku addicts need not
to worry. It has been calculated that there are 6,670,903,752,021,072,936,960 possible
arrangements. Taking into account a number symmetrical puzzles, which are essentially the same
and only differ in where the symbols are placed, there are 5,472,730,538 total possible unique
completed puzzles. This number does not include the many permutations of starting grids for a
single puzzle, which are certainly limitless.
The pleasure in solving Sudoku remains because even though each puzzle can be solved
logically and systematically, there is not a universal formula, unlike those for the Rubik’s cube
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that will solve every single arrangement no matter the difficulty in a given amount of steps. This
simple puzzle that requires no math to solve puzzles mathematicians and computer scientists
because there is no one way to solve all the puzzles, or for that matter a single puzzle. It is ironic
that the puzzle became popular because of the computerization of creating the puzzles, yet a
comparable solving technique has yet to be developed. The current approach of computers
solving Sudoku is a primitive form of trial and error. Given a grid, the program will start by
placing a 1 at the very first blank and continue checking the entire row, column and grid for
conflicts. If a conflict arises it goes back to the last block changed and increases the number by
one, repeating until the conflict is resolved. This process is extremely time consuming and
unpredictable. The time it takes to solve the same puzzle can change based on where the
computer starts making guesses.
With mathematics being an unpopular subject among children in America, it is
encouraging to see that puzzles like Sudoku inspire kids to become more interested in the subject
they typically love to hate. Even though to solve the puzzle, math concepts are not needed, the
logic behind the solution and successive feeling of accomplishment thereafter, provide a positive
reinforcement most likely not seen in a traditional math classroom. Additionally, complex
methods of solving Sudoku puzzles involve incorporating principles that involve logical
deduction like those need to solve mathematics problems [3].
Sudoku has helped not only students in middle school and high school math, but also in
college-level science courses. Organic Chemistry, a course notorious among pre-med students
for its difficulty is one example. Because of the number of chemical symbols, molecular ring
arrangements and associating the names with the molecular form memorizing them is incredibly
time consuming. By solving, Sudoku puzzles generated with the symbols and formulas,
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chemistry students report being forced to memorize all the complicated symbols and
formulations in a much faster and simple way [4]. Figure 3 shows one such puzzle created by a
professor at the University of Wisconsin.
Figure 2: Organic Chemistry as Sudoku Source: [4]
Although a puzzling problem itself, Sudoku is on its way to providing solutions to
problems in the world around us. With the number of retiring seniors steeply rising because of
the baby boomer generation, the number of people diagnosed with Alzheimer’s is expected to
increase dramatically as well. While there is no cure and genetics is likely to play a major role,
there are ways of slowing down the memory loss that comes with aging. The brain is stronger
when it is exercised just like a muscle in the body. Solving Sudoku puzzles help keep and
sometimes restore the brain’s plasticity. Studies have shown that people in the habit of playing
Sudoku report better memory and focus in other day-to-day activities [5].
Sudoku solving techniques have also helped streamline the genome mapping process. A
once tedious process involving separately tagging every single DNA sequence found in genetic
material now has become a much faster process using Sudoku solving techniques. By combining
a 2,000 year old math theorem, the Chinese Remainder Theorem, with Sudoku labeling
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numerous DNA sequences have shifted from a laborious to simple task. Every cell in the body is
programmed by DNA which in turn is several combinations of few simple codons. Just like with
only nine numbers there can be approximately 5 billion Sudoku puzzles, with a few codes there
can be more than 7 billion genetically unique individuals. By taking a grid in a Sudoku puzzle to
be a specimen and each cell within it a genotype, a completed grid can point in the direction of
missing information. The labourious task of identifying which specimen goes with which
genotype has become faster with Sudoku puzzle solving methods and computers [6].
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[1]
“Sudoku History” Conceptis Puzzles Web. 04 Apr. 2013
[2]
Pendlebury, Richard. “Can You Sudoku?” Daily Mail [London] 12 May 2005:
Print
[3]
Evans, Ryan, Lindner, Brett,Shi, Yixun. "Generating Sudoku Puzzles and its
Applications in Teaching Mathematics." International Journal of Mathematical
Education in Science and Technology 42.5 (2011): 697-704. Web. 18 Feb. 2013.
[4]
Crute, Thomas D., and Stephanie A. Myers. "Sudoku Puzzles as Chemistry
Learning Tools." Journal of Chemical Education 84.4 (2007): 612. Print.
[5]
Grabbe, Jeremy W. "Sudoku and Working Memory Performance for Older
Adults." Activities, Adaptation & Aging 35.3 (2011): 241-54. Print.
[6]
Casci, Tanita. "Technology: The Sequencing Game." Nature Reviews Genetics
10.8 (2009): 510. Print.
[7]
Aaronson, L.; , "Sudoku Science," Spectrum, IEEE , Vol.43, No.2, Pp. 16- 17,
Feb. 2006 Doi: 10.1109/MSPEC.2006.1584356 URL:
Http://ieeexplore.ieee.org.libproxy.usc.edu/stamp/stamp.jsp?tp=&arnumber=1584356&is
number=33435