You can find other difficult sudoku puzzles here, with discussion on sudoku ratings: http://www.sudoku.com/forums/viewtopic.php?t=4212 It seems that AI Escargot-Snail is anyway the most difficult (currently known) puzzle, whatever the rating. 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 Daniel Asimov Envoyé : vendredi 10 novembre 2006 07:14 À : math-fun Objet : Re: [math-fun] World's hardest sudoku puzzle? Steve Rowley wrote: << . . . On the other hand, if you mean a "typical" sudoku in the sense that it's randomly selected, then we can MEASURE that! Assuming that "difficulty" translates into computer time, which is of course dubious... . . .
There ought to be an objective measure of the *paucity* of useful information readily provided by the diagram. IDEA: If (i,j) is empty, let P(i,j) be the subset of {1,2,...,9} that does NOT appear in the union of row i, column j, and the 3x3 box containing (i,j); if (i,j) is filled with the number k, then P(i,j) = {k}. (P stands for "Possible set".) Let s(i,j) := #(P(i,j)). I propose that a good intrinsic measure of the difficulty of a Sudoku is the *geometric* mean of the 81 s(i,j)'s, since the number of possibilities is multiplicative. ---------------------------------------------------------------------------- ---------- It would be interesting to see how this measure compares with the time it takes software to solve a puzzle. --Dan _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun