## WANTED: XL Algorithm to perform BASE 9 Number Reduction

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• Looking for an XL [microsoft spread sheet] algorithm to perform BASE 9 Number reduction... BASE 9 # REDUCTION or B9#R for short is taking any integer and
Message 1 of 5 , Dec 30, 2004
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Looking for an XL [microsoft spread sheet] algorithm to perform BASE 9 Number reduction...

BASE 9 # REDUCTION or B9#R for short is taking any integer and reducing it to a single digit by adding the digits and recursively reducing sums greater than 1 digit to 1 digit...

For example:

1=1 since it is already one digit, same for 1 thru 9 of course]
7=7
11=1+1=2
27=2+7=9
84=8+4=11=1+1=2
496=4+9+6=19=1+9=10=1+0=1

You get the idea...

warmest regards,

Eric Sean Webber

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• ... Algorithm: Divide the number by 9; keep only the remainder (and replace 0 by 9). (Adding the digits is pretty fast)
Message 2 of 5 , Dec 30, 2004
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On Thu, 30 Dec 2004, Eric Sean Webber wrote:
>
> BASE 9 # REDUCTION or B9#R for short is taking any integer and reducing it to a single digit by adding the digits and recursively reducing sums greater than 1 digit to 1 digit...
>
> For example:
>
> 1=1 since it is already one digit, same for 1 thru 9 of course]
> 7=7
> 11=1+1=2
> 27=2+7=9
> 84=8+4=11=1+1=2
> 496=4+9+6=19=1+9=10=1+0=1

Algorithm: Divide the number by 9; keep only the remainder (and replace 0
by 9). (Adding the digits is pretty fast)
• Michael: Thanks for the reply. I use the term BASE 9 # Reduction loosely, as it really is a misnomer. Please see the detail of the question where you can
Message 3 of 5 , Dec 30, 2004
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Michael:

Thanks for the reply. I use the term "BASE 9 # Reduction" loosely, as it really is a misnomer. Please see the detail of the question where you can see this is not the ordinary use of the the term number BASE... Thanks !! Please see example below

Looking for an XL [microsoft spread sheet] algorithm to perform BASE 9 Number reduction...

BASE 9 # REDUCTION or B9#R for short is taking any integer and reducing it to a single digit by adding the digits and recursively reducing sums greater than 1 digit to 1 digit...

For example:

1=1 since it is already one digit, same for 1 thru 9 of course]
7=7
11=1+1=2
27=2+7=9
84=8+4=11=1+1=2
496=4+9+6=19=1+9=10=1+0=1

You get the idea...

warmest regards,

Eric Sean Webber

Michael G Gian <work.gian@...> wrote:

-----Original Message-----

Looking for an XL [microsoft spread sheet] algorithm to perform BASE 9 Number reduction...

Eric Sean Webber

Eric,

In my version, (9.0.6926 SP-3), the function MOD(number, divisor) works for numbers up to 1,207,959,551.

This is (2^30 + 2^27 � 1) for what that is worth. Larger numbers return the dreaded #NUM!

Write the cell =IF(MOD(number, 9)=0, 9, MOD(number,9)) in order to change 0s to 9s.

number can refer to another cell for easy repeated entry.

I have no experience getting Excel to play with large integers. Mathematica for that.

Michael

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• ... To find the digital root of a number. place your number in cell A1 and type this formila in another cell for the digital root.
Message 4 of 5 , Dec 30, 2004
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>From: Chris Caldwell <caldwell@...>
>To: Eric Sean Webber <ericswebber@...>
>Subject: Re: [PrimeNumbers] WANTED: XL Algorithm to perform BASE 9 Number
>Reduction
>Date: Thu, 30 Dec 2004 08:26:54 -0600 (CST)
>
>On Thu, 30 Dec 2004, Eric Sean Webber wrote:
> >
> > BASE 9 # REDUCTION or B9#R for short is taking any integer and reducing
>it to a single digit by adding the digits and recursively reducing sums
>greater than 1 digit to 1 digit...
> >
> > For example:
> >
> > 1=1 since it is already one digit, same for 1 thru 9 of course]
> > 7=7
> > 11=1+1=2
> > 27=2+7=9
> > 84=8+4=11=1+1=2
> > 496=4+9+6=19=1+9=10=1+0=1
>
>Algorithm: Divide the number by 9; keep only the remainder (and replace 0
>by 9). (Adding the digits is pretty fast)

To find the digital root of a number.

place your number in cell A1 and type this formila in another cell for the
digital root.
=IF(A1-INT(A1/9)*9,A1-INT(A1/9)*9,9)

You can use the =IF(MOD(\$A\$1,9),MOD(\$A\$1,9),9) but it is only good to 9
places

if you want to make a project
extract the digits using
=IF(ISERR(VALUE(MID(TEXT(\$A\$1,0),B3,1))),0,VALUE(MID(TEXT(\$A\$1,0),B3,1)))
place in C3 and 1-15 in cells B3-B17 and copy it down.

sum cells C3..C7 and copy that in A19
The place
=IF(ISERR(VALUE(MID(TEXT(\$A\$19,0),B19,1))),0,VALUE(MID(TEXT(\$A\$19,0),B19,1)))
in C19, 1,2,3 in cells B19..B23 and copy down
and sum those in cell A24
then place
=IF(ISERR(VALUE(MID(TEXT(\$A\$24,0),B24,1))),0,VALUE(MID(TEXT(\$A\$24,0),B24,1)))
in cell C24 1,2 in cells B24,B25 and copy down

This last step should only require one formula copy.

Finally, you can write a VB function Droot() to have available on the fly. I
used Dr. C's method. Of
course you can do the digital parse this way too.

Function Droot(s As String) As Double
Dim x As Double
x = Evaluate(s)
x = x - Int(x / 9) * 9
If x > 0 Then
Droot = x
Else
Droot = 9
End If
End Function

A function is the way to go for this.

I have attached a worksheet.

Have fun in the facinating world of numbers
Cino

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• In message , Eric Sean Webber writes ... Cool. -- Ben Newsam
Message 5 of 5 , Dec 31, 2004
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In message <20041231011323.18121.qmail@...>, Eric
Sean Webber <ericswebber@...> writes
>8+4=11

Cool.
--
Ben Newsam
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