A Group-Permutation Algorithm to Solve the Generalized SUDOKU

Sudoku is a game with numbers, formed by a square with the side of 9, and on each row and column are placed the digits 1, 2, 3, 4, 5, 6, 7, 8, 9, written only one time; the square is subdivided in 9 smaller squares with the side of 3×3, which, also, must satisfy the same condition, i.e. each square to contain all digits from 1 to 9 written only once. The Japanese company Nikoli has popularized this game in 1986 under the name of sudoku, meaning “single number”. Sudoku can be generalized to squares whose dimensions are 2n × n2, where 2n ≥ , using various symbols (numbers, letters, mathematical symbols, etc.), written just one time on each row and on each column; and the large square is divided into 2n small squares with the side n × n and each will contain all 2n symbols written only once. An elementary solution of one of these generalized Sudokus, with elements (symbols) from the set {}1 2 1 2 ^2 , ,..., , , ..., , ..., n n n nS s s s s s s+= (supposing that their placement represents the relation of total order on the set of elements S), is: Row 1: all elements in ascending order 1 2 1 2 ^2, ,..., , , ..., , ..., n n n ns s s s s s+ On the next rows we will use circular permutations, considering groups of n elements from the first row as follows