And of course 9*(B-1) + A generates another bimagic square. 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 : vendredi 4 novembre 2005 18:36 À : 'math-fun' Objet : [math-fun] Sudokus and bimagic squares Bonjour, There is a link between sudokus and bimagic squares (magic squares remaining magic when the numbers are squared). Sudoku A: 258 147 369 147 369 258 369 258 147 825 714 936 714 936 825 936 825 714 582 471 693 471 693 582 693 582 471 Sudoku B: 294 618 753 753 294 618 618 753 294 942 186 537 537 942 186 186 537 942 429 861 375 375 429 861 861 375 429 Apply 9*(A-1) + B, you get: 11 45 67 6 28 62 25 50 75 7 32 57 20 54 76 15 37 71 24 46 80 16 41 66 2 36 58 72 13 38 55 8 33 77 21 52 59 3 34 81 22 47 64 17 42 73 26 51 68 12 43 63 4 29 40 65 18 35 60 1 48 79 23 30 61 5 49 74 27 44 69 10 53 78 19 39 70 14 31 56 9 This square is bimagic with: 1) consecutive integers from 1 to 81. 2) magic, sum S1 = 369. 3) and more interesting: square each number, and the square remains magic, sum S2 = 20049. Of course, it does not work for each couple of sudokus, i.e. if you want that the generated square use distinct integers. I will add a page on that, in the next update of multimagie.com Christian. _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun