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 <boppo@cco.caltech.edu> <boppo@cco.caltech.edu> 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


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