tag:blogger.com,1999:blog-264226589944705290.post3752963953089784625..comments2023-11-05T03:45:25.001-08:00Comments on God Plays Dice: A cute number theory puzzleMichael Lugohttp://www.blogger.com/profile/15671307315028242949noreply@blogger.comBlogger7125tag:blogger.com,1999:blog-264226589944705290.post-36972986699399944852011-08-16T23:15:35.246-07:002011-08-16T23:15:35.246-07:00I find
77x78 = 006006
286x287 = 082082
363x364 ...I find <br />77x78 = 006006<br />286x287 = 082082<br />363x364 = 132132<br />637x638 = 406406<br />714x715 = 510510<br />923x924 = 852852<br />all by a program with HP 11.<br /><br />The results are always going to have 1001 = 7x11x13 as a factor.Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-45010786866466386572011-07-07T21:00:34.759-07:002011-07-07T21:00:34.759-07:00Besides Jonathan's, I also found 637*638 = 406...Besides Jonathan's, I also found 637*638 = 406406. A key to my solutions, and I think all potential solutions, is that the final product has to be a multiple of 1001 in order to have "concatenation". 1001 is conveniently 7*11*13, and so I tried multiples of 77, multiples of 91, and multiples of 143. In general, any concatenations would be multiples of 11, 101, 1001, 10001, 100001, etc. Or repeated concatenations might be multiples of 111, 10101, 1001001, and so on.Rocky Roerhttps://www.blogger.com/profile/17833205290061997823noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-13037794723936760922011-07-07T14:47:40.072-07:002011-07-07T14:47:40.072-07:00Looks like they're rarer than I expected, with...Looks like they're rarer than I expected, with only one four digit and one five digit generator.<br /><br />I was going to find more, but then decided to use the awesome power of OIES:<br /><br />http://oeis.org/A116285<br /><br />There are some very interesting patterns in that sequence, like the fact that 363, 336633, and 333666333 are all generators. That begs to be explored...Jon Ingramhttps://www.blogger.com/profile/02922696891178333845noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-14935129029335266042011-07-07T14:41:14.813-07:002011-07-07T14:41:14.813-07:00Jonathan: those are some, but not all, of the answ...Jonathan: those are some, but not all, of the answers.Michael Lugohttps://www.blogger.com/profile/01950197848369071260noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-87265578148060411552011-07-07T14:39:11.512-07:002011-07-07T14:39:11.512-07:00I get 2 or 3 answers depending on weather you'...I get 2 or 3 answers depending on weather you're willing to write xy as 0xy or not. <br /><br />SPOLIERS ALERT<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br />.<br /><br />.<br />.<br />.<br />.<br />.<br /><br /><br />.<br />.<br />.<br />.<br />.<br />.<br />.<br /><br />..<br />.<br />.<br />.<br />.<br />.<br />.<br />074*075=006006<br />286*287=082082<br />363*364=132132Anonymoushttps://www.blogger.com/profile/10716393385703376978noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-84714294464072043782011-07-07T14:28:18.755-07:002011-07-07T14:28:18.755-07:00Also, some other palindromes:
81818 and 336633Also, some other palindromes:<br /><br />81818 and 336633Bryanhttps://www.blogger.com/profile/00161448428728145065noreply@blogger.comtag:blogger.com,1999:blog-264226589944705290.post-82049053644017219152011-07-07T14:27:27.712-07:002011-07-07T14:27:27.712-07:00The most interesting number I got after generalizi...The most interesting number I got after generalizing the problem in, what I assume to be, a pretty standard way:<br /><br />7272727Bryanhttps://www.blogger.com/profile/00161448428728145065noreply@blogger.com