0,3

An n^2 X n^2 sudoku is an n^2 X n^2 array which is subdivided into n^2 n X n subarrays. Each row and column of the full array must contain each of the numbers 1 ... n^2 exactly once (this makes it a Latin square of order n^2). In addition, each of the n^2 n X n subarrays must also contain each of the numbers 1 ... n^2 exactly once.

K. Ying Lin, "Number Of Sudokus" in 'Journal of Recreational Mathematics' pp. 120-4 Vol.33 No. 2 2004-5 Baywood Pub. Amityville NY.

Bertram Felgenhauer and Frazer Jarvis, There are 6670903752021072936960 Sudoku grids

J. P. Grossman, Javascript Sudoku solver

Ed Pegg Jr, Sudoku variations

Ed Russell and Frazer Jarvis, There are 5472730538 essentially different Sudoku grids

Wikipedia, Sudoku

Eric Weisstein's World of Mathematics, Sudoku

Comment from Hugo van der Sanden (hv(AT)crypt.org), Jun 12 2005: "Consider n=2: renumbering doesn't affect the result, so we can fix row A at (1, 2, 3, 4) and multiply the result by 4!. Once rows B and C are chosen, there is only one option for row D. Row B must have (3, 4) or (4, 3) followed by (1, 2) or (2, 1).

"Rows C and D can be swapped without affecting validity, so we can fix column 1 of row C to be the lower of the two options and multiply the results by 2.

"That leaves at most 4 options for row C (2 choices in each of the remaining 3 positions, of which one must have our selected number as one of the choices); that leaves 16 options to check for rows B and C, the result to be multiplied by 48.

"Checking, we find just 6 of the 16 grids are valid:

1234/3412/2143/4321 1234/3412/2341/4123 1234/3421/2143/4312

1234/4312/2143/3421 1234/4321/2143/3412 1234/4321/2413/3142

so a(2) = 6 * 48 = 288."

An example of a sudoku of size 9 X 9:

124|567|893

378|294|516

659|831|742

---+---+---

987|123|465

231|456|978

546|789|321

---+---+---

863|972|154

495|618|237

712|345|689

Cf. A109741.

Sequence in context: A037946 A047805 A008695 this_sequence A008367 A112077 A114762

Adjacent sequences: A107736 A107737 A107738 this_sequence A107740 A107741 A107742

nonn,bref

Richard McNair (rmcnair(AT)ntlworld.com), Jun 11 2005

Entry revised by njas, Aug 12 2005

Thanks to Emiliano Venturini (il_wentu(AT)excite.com), for some corrections to the comments, Apr 08 2006