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Subject:
From:
Lewis Pike <[log in to unmask]>
Reply To:
Informal Science Education Network <[log in to unmask]>
Date:
Sat, 22 Nov 2003 17:24:17 +0000
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ISEN-ASTC-L is a service of the Association of Science-Technology Centers
Incorporated, a worldwide network of science museums and related institutions.
*****************************************************************************

You are looking for the lowest common multiple of the numbers of
different choices until you get repeats - actually that is easier to do
for primes than for a set of non-primes, because as you have done for
the primes all you need to do is multiply them together.

The 'proper' way to do it is to prime factorise all of the numbers (so
4 becomes 2^2 because 2 is a prime, and there is an extra 2 left over,
whilst 6 becomes 2 X 3 which are the prime factors). Then from each of
the numbers you take the highest available power of each of the primes
and multiply these together to get the LCM.

so for 1-6 you get 1, 2, 3, 2^2, 5, 3X2 giving you the LCM of 2^2 X 3 X
5 or 60 as you worked out. The reason the primes make it easy is you
know before you start that the numbers are all prime anyway, so you can
just multiply them together.

Lewis.

On 21 Nov 2003, at 23:20, Clifford Wagner wrote:

> 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
>
> ***********************************************************************
> More information about the Informal Science Education Network and the
> Association of Science-Technology Centers may be found at
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