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By Terry Solomon
Sudoku puzzles have always boasted that it is a brain
stimulating game that requires no mathematical skills. In
essence, the statement is correct because a player does not
really have to add numbers, columns or rows to play Sudoku
puzzles.
However, if we look at the game of Sudoku puzzles more
closely,
we can actually identify some basic reference to concepts that
are of purely mathematical nature. For instance, Sudoku games
usually have several blocks or squares that are already filled
up with certain numbers. But what if we start from a totally
blank grid, meaning no given numbers at all? The question then
will be how many ways can the solution be achieved given the
rules set forth by the puzzle game? If we go by the simple 4
by
4 Sudoku grid, there are a total of 576 ways of arranging the
numbers 1, 2, 3, 4. in a square or block presentation with
each
number appearing only once in every row and column. However,
Frazer Jarvis of the University of Sheffield was able to come
up with 88 valid arrangements for the very same grid and
subsequently posted his observations on the Sudoku Programmers
Forum.
Clearly, logic is not the only factor at work in Sudoku
puzzles. Mathematics is also a key player. Ditto with various
rules. Sudoku said it only has one basic rule, but when you
sit
down and try to solve the puzzle, various rules as well as
techniques will crop up that you can find useful as you try to
uncover the enigma of the game. While Sudoku's basic rule will
help in getting the correct solution, repeated application of
this one basic rule can make the game one big bore. Barry
Cipra, a mathematician and writer from Northfield, Minnesota,
said the Sudoku rules actually have several hierarchies. These
rules get more complicated as the puzzle becomes more complex
as in the case of 10 by 10, 12 by 12, and 14 by 14 grids. The
basic rules, Cipra said, apply only to the standard 9 by 9
grid. Higher levels of the puzzle mean more complex rules.
Nevertheless, the fun begins when a player is able to discover
patterns that will trigger the application of the rules
The concept of Sudoku puzzles about no mathematics required is
thus a bit flawed. What the game actually wants to say is that
no arithmetic is really required, meaning no counting of 1, 2,
3, 4, and so on. Sudoku puzzles also say it only has one
simple
rule, which is, to fill in the grid with numbers ranging from
1
through 9 in such a way that every row and column will have
one
instance each of the said digits. Again, there is error here,
because sticking too rigidly to this one simple rule will not
help a player to easily solve the puzzle. Analytical methods,
including the discovery of unwritten rules and tactics, are
needed to see the game to its logical conclusion.
About The Author: For more valuable information on sudoku
puzzles please visit www.sudoku-puzzles.com
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