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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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