Message: 1994/08/26-004655 *From: stadler@math.ohio-state.edu (Jonathan Stadler)* *Organization: Department of Mathematics, The Ohio State University* *Date: 25 Aug 1994 19:46:55 -0400* *Subject: Re: High throws...* *Message-Id: <33jahf$d5h@math.mps.ohio-state.edu>* *References: <199408252312.QAA18129@accord.cco.caltech.edu> <199408252312.QAA18129@accord.cco.caltech.edu>* In article <199408252312.QAA18129@accord.cco.caltech.edu> <199408252312.QAA18129@accord.cco.caltech.edu>, Bruce G. Tiemann wrote: >6 balls: 11 6 10 5 12 8 0 3 1 9 7 4 2 (courtesy of me - I dare you to >generate a list of tricks that includes it, as it has every throw >from 0 - 12 inclusive, once only, in its thirteen throws. Thus, >you can't exclude any, though it is ground state. I did however make it >deliberately easy by giving one hand all the double digit throws, >early on so it would be downhill from throw #5, and it gets rid of >the annoying 3 in a 3 1 (which aren't so bad). Note that it is an >isomer of 7 8 9 10 11 12 0 1 2 3 4 5 6 - I'm looking for a good name >for these tricks - those that have every throw from 0 - 2n, once only, >inclusive. How about difficult? > For those people who don't like high throws or widely differing >throw heights, look elsewhere! >7 balls: 10 10 1. So easy, yet soooo difficult. > -boppo If you want a few of those difficult 0-2n patterns, try these: If the numbers m+1 and 2k+1 are relatively prime, (i.e. have no common factor other than one), then 1 m+1 2m+1 ... 2km+1 (mod 2k+1) is a valid site-swap pattern. Now try some! For example, k=m=4, you get: 1 4+1 2*4+1 ... 2*4*4+1 (mod 9) gives: 1 5 0 4 8 3 7 2 6 Jon Stadler stadler@math.ohio-state.edu ------------------------------------------------------------------------ Message: 1994/08/26-004655 / Juggling Information Service / jis@juggling.org