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Clifford:

Your suggestion of primes makes sense -- you'll get more
recombinations. But realize that 9 is NOT prime. If you have 3 and 9
together, they will always be paired together. You could delete
either one and have a reasonable set that would constantly mix. As
mentioned, you'd be multiplying the primes to make the least common
denominator. If you choose to go with 1, 2, 3, 5, and 7, you'll get
210 options. If you choose 1, 2, 5, 7, and 9, you'll get 630 options
(the SAME as if you had the sequence you suggested, with both 3 and
9). If you need six word groups, try adding 11, which is the next
prime, in place of either 3 or 9. That would give you 2310 or 6930
possible word groupings respectively.

Hope that helps.

Kodi

>ISEN-ASTC-L is a service of the Association of Science-Technology Centers
>Incorporated, a worldwide network of science museums and related institutions.
>*****************************************************************************
>
>P in my exhibit Contraptions A to Z is for Poetry machine.  A visitor at the
>museum it's presently at asked what's the formula for figuring out how many
>turns it takes to repeat a sentence?  Anyone have a simple formula?
>
>The words are on cards mounted on chains so that each time visitors turn the
>crank, a new sentence is created along the top line. Below are the words in
>the machine.  It takes 60 turns to get a repeat sentence in this arrangement
>(of 1,2,3,4,5,6 words on the six chains).  I know 60 is the lowest number
>1,2,3,4,5,6 all evenly divide into, but how do you figure out what that
>number is, quickly?
>
>I knew shortly after I built it I should have done it with prime numbers
>(1,2,3,5,7,9 words on the six chains) so that each word would eventually go
>with every other word in the machine.  (As it is "your" always matches up
>with pirates" and "parents", never "poodles" or "penguins" etc.)  I've
>puzzled out 630 as (I think) the smallest number the six primes each divide
>into.  Would that then indeed be the number of different sentences one would
>get before a repeat with this prime arrangement?  I and at least one other
>curious visitor thank you for any enlightenment you can give us.
>
>and      your      perky       pirates       danced     forever
>             my        wacky     poodles      lived        wildly
>                         punk        parents       ate           perfectly
>                                        penguins     sang         laughingly
>                                                          played      upside
>down
>
>everywhere
>
>Clifford Wagner
>www.scienceinteractives.com
>
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