[math-fun] Pandiagonal Sudoku?
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.
I don't know of one being previously published. Might be an interesting puzzle, with the alphabet instead of numbers. Ed Pegg Jr 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
Bonjour Ed, Good idea to construct a puzzle. But seems difficult to get an "interesting" puzzle in my case. The square has a lot of symmetries, similar patterns, owing to its pandiagonal characteristics. Looking at, say, the two or three first sub-squares, people should be able understand the construction method and finish directly the full square. But I will think more deeply about your idea of puzzle. 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 Xeipon Envoyé : lundi 6 mars 2006 18:27 À : math-fun Objet : Re: [math-fun] Pandiagonal Sudoku? I don't know of one being previously published. Might be an interesting puzzle, with the alphabet instead of numbers. Ed Pegg Jr 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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
If you want to see a 25x25 example, the smallest possible pandiagonal Sudoku: published in the April 2006 issue, page 70, of Mathematics Today (IMA, the Institute of Mathematics and its Applications, UK). In the same issue, the second part of the article on pandiagonal magic squares published by Dame Kathleen Ollerenshaw. 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 Christian Boyer Envoyé : lundi 6 mars 2006 18:21 À : 'math-fun' Objet : [math-fun] Pandiagonal Sudoku? 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
I can send you a scan of my 25x25 example published in their issue. Impossible through [math-fun]. Send me a direct message. 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 Christian Boyer Envoyé : samedi 1 avril 2006 09:39 À : 'math-fun' Objet : RE: [math-fun] Pandiagonal Sudoku? If you want to see a 25x25 example, the smallest possible pandiagonal Sudoku: published in the April 2006 issue, page 70, of Mathematics Today (IMA, the Institute of Mathematics and its Applications, UK). In the same issue, the second part of the article on pandiagonal magic squares published by Dame Kathleen Ollerenshaw. 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 Christian Boyer Envoyé : lundi 6 mars 2006 18:21 À : 'math-fun' Objet : [math-fun] Pandiagonal Sudoku? 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 _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
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