tag:blogger.com,1999:blog-5730391.post1501585773645200335..comments2020-02-27T17:39:53.901-08:00Comments on Blaine's Puzzle Blog: Billiard Balls PuzzleBlainehttp://www.blogger.com/profile/06379274325110866036noreply@blogger.comBlogger4125tag:blogger.com,1999:blog-5730391.post-11307415760304952452008-05-02T09:53:00.000-07:002008-05-02T09:53:00.000-07:00I'm assuming he took the 1001 ways and assumed the...I'm assuming he took the 1001 ways and assumed the 15 ball was fixed, leaving 4! ways to arrange the other balls. As you pointed out, this should be 1001 times 5! since we don't know where the 15 ball should go. (Then after that you can divide by 2 for the reflection).<BR/><BR/>So I'm curious. Eric, did you use the "brute-force" method or another?Blainehttps://www.blogger.com/profile/06379274325110866036noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-75843709022547282732008-05-02T08:20:00.000-07:002008-05-02T08:20:00.000-07:00I'm not sure how ericmargel got 24,000 permutation...I'm not sure how ericmargel got 24,000 permutations to test for the top line.<BR/><BR/>My reasoning is that there are 60,060 configurations of the top line to test. Here's the idea, there are 15 balls, the 15 must go on the top row leaving 4 choices from 14 to be made (1,001 ways). Once those have been made there are 5!=120 ways to arrange the balls along the top row. But since we're not interested in reflections, we divide by 2 since each configuration of the top row is equivalent to one other. So there are<BR/><BR/>1001 * 120 / 2 = 60,060 ways to configure the top row.Erichttps://www.blogger.com/profile/00478789589953835840noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-56973242759898567872008-04-30T10:20:00.000-07:002008-04-30T10:20:00.000-07:006 14 15 3 138 1 12 107 11 24 956 14 15 3 13<BR/>8 1 12 10<BR/>7 11 2<BR/>4 9<BR/>5Erichttps://www.blogger.com/profile/00478789589953835840noreply@blogger.comtag:blogger.com,1999:blog-5730391.post-47953496397946121292008-03-27T13:13:00.000-07:002008-03-27T13:13:00.000-07:00I haven't come up with a solution yet.It shouldn't...I haven't come up with a solution yet.<BR/>It shouldn't be too hard to brute-force it with a computer program... since the 15 must go on the top line, there's only 24,000 permutations of the top line to test. <BR/><BR/>But someone's got to have a better idea!EricMargelhttps://www.blogger.com/profile/02090556952649043090noreply@blogger.com