Re: [math-fun] Pandiagonal Sudoku?
I generated pandiagonal latin squares of size 17*17 some time ago. _http://groups.yahoo.com/group/magiccubes/_ (http://groups.yahoo.com/group/magiccubes/) The same method was already too slow for 19*19 AFAIR, but some heuristics to find _some_ solutions could be feasable. Maybe searching with the additional 5*5-squares constraint too. You can make these from 25-queen solutions and some other tricks. There could be something in the paper from Jordan Bell Guenter. --------------------------------------------------------- Christian Boyer <cboyer@club-internet.fr> wrote: Do you know if a pandiagonal Sudoku has already been published? I have a 25x25 example, the smallest possible size for this problem, but perhaps the same work has already been done. "Pandiagonal Sudoku" means that all the diagonals and broken diagonals of the square should also contains all the numbers, as it is for rows, columns, and sub-squares. It is proved that a pandiagonal Latin square cannot exist for 2k and 3k orders, meaning that a pandiagonal Sudoku of standard size (9x9) is impossible. I know published 25x25 pandiagonal Latin squares, but they are not Sudokus, because they are not organized in 5x5 sub-squares. Christian.
Bonjour Guenter, Examples of pandiagonal Latin squares of prime orders > 3 are easy to construct, including 17*17 and 19*19. Here is one of the numerous methods. In the first row, write the numbers. Write the second row using the first row shifted by x elements, 1 < x < order-1. Write the third row using the second row shifted by the same number of elements. And so on... Here is a 5*5 pandiagonal Latin square constructed with that method, shifting the rows by 2 elements: 1 2 3 4 5 3 4 5 1 2 5 1 2 3 4 2 3 4 5 1 4 5 1 2 3 Christian. -----Message d'origine----- De : math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com [mailto:math-fun-bounces+cboyer=club-internet.fr@mailman.xmission.com] De la part de Sterten@aol.com Envoyé : mardi 7 mars 2006 17:17 À : xeipon2@yahoo.com; math-fun@mailman.xmission.com Objet : Re: [math-fun] Pandiagonal Sudoku? I generated pandiagonal latin squares of size 17*17 some time ago. _http://groups.yahoo.com/group/magiccubes/_ (http://groups.yahoo.com/group/magiccubes/) The same method was already too slow for 19*19 AFAIR, but some heuristics to find _some_ solutions could be feasable. Maybe searching with the additional 5*5-squares constraint too. You can make these from 25-queen solutions and some other tricks. There could be something in the paper from Jordan Bell Guenter. --------------------------------------------------------- Christian Boyer <cboyer@club-internet.fr> wrote: Do you know if a pandiagonal Sudoku has already been published? I have a 25x25 example, the smallest possible size for this problem, but perhaps the same work has already been done. "Pandiagonal Sudoku" means that all the diagonals and broken diagonals of the square should also contains all the numbers, as it is for rows, columns, and sub-squares. It is proved that a pandiagonal Latin square cannot exist for 2k and 3k orders, meaning that a pandiagonal Sudoku of standard size (9x9) is impossible. I know published 25x25 pandiagonal Latin squares, but they are not Sudokus, because they are not organized in 5x5 sub-squares. Christian. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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