SUDOKU: LOGICAL NUMBER PUZZLE DEVOID OF ARITHMETIC 1
MAT 135 Final Paper Strand One - J.D. Thomason
Strand One: Historical Significance
An examination of the history of the Sudoku puzzle should begin with a clarification of its ancestral roots. Sudoku is commonly mistaken as a derivation of the magic square, in which the sum of every diagonal, row, and column of a grid adds up to the same number. Other than the fact that Sudoku takes place on a grid, this assumption could not be further from the truth. The true ancestor to Sudoku is a combinatorial object known as a Latin square (Delahaye, 2006; Hirst, 2016).
A Latin square is a matrix of n
2
cells arranged in a grid with n cells on each side. Such a matrix with n cells on each side is said …show more content…
A completed Latin square. Neither rows nor columns are allowed to contain duplicate symbols.
The primary separation that Sudoku has from the magic square is the way in which the puzzle is solved. At first glance, a typical Sudoku puzzle looks like a standard Latin square
SUDOKU: LOGICAL NUMBER PUZZLE DEVOID OF ARITHMETIC 2 of order 9. Due to the nature of Sudoku’s rules, this is not entirely true. A typical Sudoku grid is divided into nine 3x3 sub-grids, which is a bit of a departure from the traditional
Latin square. True to its inspiration, however, symbols are to be placed on the grid in such a way that numbers are not allowed to repeat in rows, columns, or within the aforementioned 3x3 sub-grids; this is illustrated in Figure 2. Strangely, conforming to the rules of a typical Sudoku puzzle requires no arithmetic, even though the symbols used in the puzzle are usually numbers. Consequently, Sudoku is definitely not a derivative of the magic square.
Figure 2 . A Sudoku grid layout. Symbols must remain unique throughout each row, column, and 3x3 sub-grid.
The origins of Sudoku are not entirely clear. It is speculated that the earliest publishing of modern-day Sudoku is said to have been in an issue of Dell Pencil Puzzles
MAT 135 Final Paper Strand One - J.D. Thomason
Strand One: Historical Significance
An examination of the history of the Sudoku puzzle should begin with a clarification of its ancestral roots. Sudoku is commonly mistaken as a derivation of the magic square, in which the sum of every diagonal, row, and column of a grid adds up to the same number. Other than the fact that Sudoku takes place on a grid, this assumption could not be further from the truth. The true ancestor to Sudoku is a combinatorial object known as a Latin square (Delahaye, 2006; Hirst, 2016).
A Latin square is a matrix of n
2
cells arranged in a grid with n cells on each side. Such a matrix with n cells on each side is said …show more content…
A completed Latin square. Neither rows nor columns are allowed to contain duplicate symbols.
The primary separation that Sudoku has from the magic square is the way in which the puzzle is solved. At first glance, a typical Sudoku puzzle looks like a standard Latin square
SUDOKU: LOGICAL NUMBER PUZZLE DEVOID OF ARITHMETIC 2 of order 9. Due to the nature of Sudoku’s rules, this is not entirely true. A typical Sudoku grid is divided into nine 3x3 sub-grids, which is a bit of a departure from the traditional
Latin square. True to its inspiration, however, symbols are to be placed on the grid in such a way that numbers are not allowed to repeat in rows, columns, or within the aforementioned 3x3 sub-grids; this is illustrated in Figure 2. Strangely, conforming to the rules of a typical Sudoku puzzle requires no arithmetic, even though the symbols used in the puzzle are usually numbers. Consequently, Sudoku is definitely not a derivative of the magic square.
Figure 2 . A Sudoku grid layout. Symbols must remain unique throughout each row, column, and 3x3 sub-grid.
The origins of Sudoku are not entirely clear. It is speculated that the earliest publishing of modern-day Sudoku is said to have been in an issue of Dell Pencil Puzzles