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Newsgroups: fido.science
Distribution: fido
From: Jasen Betts 
Date: Fri, 10 Sep 04 07:45:50 +0200
Subject: Approaches
Message-ID: 
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Xref: number1.nntp.dca.giganews.com fido.science:330

Hello Miles.

10 Sep 04 05:14, you wrote to me:

 MM> G'morning Jason,

 MM> I got an opportunity to read through your steps there, and to
 MM> meditate on differences of approach.

 MM> Did you scratch-pad your run in the message itself, or use a
 MM> spreadsheet on the side ?

no spreadsheet, most of the arithmetic was done in bash (the linux
command-line)

eg: the the list of squares divisible by nine was done like this

 done > somefile

 MM> My run at it,  having checked out the arithmetic,  lay in using qb
 MM> to check out, what values of TEN would produce a one-less square
 MM> divisible by 9 ... 145, 325, 730 and 901.

I started with squares divisible by 9 as they were easy to predict.

initially I calculated them by hand, but then gave up and used the computer (as
it was before breakfast and my brain was underperfrming.

n=12: while [ x lt 32 ] do echo $x  $((x*x))  $((x*x+1)) ; x=$((x+3));

which after berakfast it shouldn't have been difficult to do on paper.

 MM> I used these values in another qb scratcher to test for values of
 MM> I and Y that would see SIX squares between TEN and NINETY for each
 MM> of the possible TENs, and bingo-ed into the solution.

I didn't, first I rejected 730  (because N=0) and that's no good for NINETY

 MM> Using qb this way is a far cry from the mind-stretching logic that
 MM> a 1960's Scientific American puzzle from Martin Gardner demanded
 MM> to solve...

yeah, I think my approach of determineing possible NINETYs (given divisibility
by 9. there were about 20 I think) and then doing some suqare roots to kick out
value s of SIX i probably closer to the preferred method.


 MM> EVE/DID = .TALKTALKTALK....

in other words

 EVE/DID = TALK/9999

on my handy command line the using the tool "factor" on 9999
gives me 3 3 11 101

so  I= 0
    D is 1,3,or 9

D cant be 1 as EVE < DID

hmm, what should I do next, there's still over 180 possible combinations for
E,V and D

depending on the value for DID

EVE*11 = TALK  or EVE*33 =TALK
DID*11 = 9999     DID*33 =9999

clearly EVE*11 results in E=K which is not allowed so it must be EVE*33
which means DID=9999/33=303

 so given EVE