multiples of 9
makc.th...@gmail.com
9. for example:
n 9n
1 9 obvious
2 18 1+8=9
3 27 2+7=9
4 36 3+6=9
5 45 4+5=9
6 54 5+4=9
7 63 6+3=9
8 72 7+2=9
9 81 8+1=9
10 90 obvious
how is this explained mathematically? could it be used somehow? perhaps
to speed up multiplication or something.
?
Virgil
"makc.th...@gmail.com" <makc.th...@gmail.com> wrote:
Before the advent of electronic shortcuts to manual arithmetic, it was
widely used to check arithmetical operations, particularly
multiplications, in a technique called casting out nines.
You can google "casting out nines for a lot more that you probably will
ever want to know about the process.
me1...@gmail.com
Your number X = A + 10B + 100C + ... + (10^d)D. If X is a multiple of
9, then X minus (9B + 99C + ... + (10^d - 1)D) gives us another
multiple of 9. After the subtraction, you have A+B+C+...+D, which is
the sum of the digits.
Bob H
makc.th...@gmail.com
a ha! thanks man, i knew that must be simple.
i opened my calc and did 123x9, which is 1107, 1+1+0+7 = 9, and was
under impression that it is always 9, but then i did 321x9 :(
so it is actually sum of digits of sum of digits of. .... .. . . digits
of 9n = 9.
that's so cool that I almost have an erection. cant wait to tell my
mommy.
Arturo Magidin
makc.th...@gmail.com <makc.th...@gmail.com> wrote:
>
>me1...@gmail.com wrote:
>> makc.th...@gmail.com wrote:
>> > I have just noticed that for numbers like 9n, sum of difits is always
>> > 9. [-SNIP-] how is this explained mathematically?
>>
>> Your number X = A + 10B + 100C + ... + (10^d)D. If X is a multiple of
>> 9, then X minus (9B + 99C + ... + (10^d - 1)D) gives us another
>> multiple of 9. After the subtraction, you have A+B+C+...+D, which is
>> the sum of the digits.
>
>a ha! thanks man, i knew that must be simple.
>
>i opened my calc and did 123x9, which is 1107, 1+1+0+7 = 9, and was
>under impression that it is always 9, but then i did 321x9 :(
Keep doing it until you get a single digit answer. Then that answer is
either 9 or 0 (and it is only 0 if you started by multiplying by 0...)
>so it is actually sum of digits of sum of digits of. .... .. . . digits
>of 9n = 9.
Yes.
--
======================================================================
"It's not denial. I'm just very selective about
what I accept as reality."
--- Calvin ("Calvin and Hobbes" by Bill Watterson)
======================================================================
Arturo Magidin
magidin-at-member-ams-org
mensa...@aol.com
Of course, casting out 9's is just the tip of the iceberg.
See Slot Machine Arithmetic: Casting Out Cherries
<http://members.aol.com/rotanasnem/cherries/cherries.htm>
Prai Jei
<eh869u$2tgm$1...@agate.berkeley.edu>:
>>i opened my calc and did 123x9, which is 1107, 1+1+0+7 = 9, and was
>>under impression that it is always 9, but then i did 321x9 :(
>
> Keep doing it until you get a single digit answer. Then that answer is
> either 9 or 0 (and it is only 0 if you started by multiplying by 0...)
You can play this game with multiplications also, in which case you *can*
get a zero answer even if the starting number is non-zero, e.g. 25 -> 10 ->
0.
This leads to a *very* uneven distribution of final numbers, with "0"
leading the field (since any intermediate number containing 0 promptly
leads to a final answer of 0) and even digits faring better than odd with
"1" being extremely rare.
The number 277,777,788,888,899 requires no less than 11 cycles before a
single digit (0) is reached. It is the smallest such number. No number
requiring more than 11 cycles is known - there are none up to 10^51.
--
Warning: keel away from child for hot bulb
Interchange the alphabetic letter groups to reply
Proginoskes
You can't wait to tell your mommy that you almost have an erection?
What kind of sick bastard _are_ you?
--- Christopher Heckman
mensa...@aol.com
Mother/son incest is a common category of porn site.
So they say.
>
> --- Christopher Heckman
Prai Jei
<1161297176.9...@i42g2000cwa.googlegroups.com>:
>> that's so cool that I almost have an erection. cant wait to tell my
>> mommy.
>
> You can't wait to tell your mommy that you almost have an erection?
> What kind of sick bastard _are_ you?
He's not sick he's absolutely normal. It used to happen to me when I was a
kid.
makc.th...@gmail.com
Prai Jei wrote:
> Proginoskes (or somebody else of the same name) wrote thusly in message
> <1161297176.9...@i42g2000cwa.googlegroups.com>:
>
> >> that's so cool that I almost have an erection. cant wait to tell my
> >> mommy.
> >
> > You can't wait to tell your mommy that you almost have an erection?
> > What kind of sick bastard _are_ you?
>
> He's not sick he's absolutely normal. It used to happen to me when I was a
> kid.
are you saying you havent had an erection ever since then?
Prai Jei
message <1161587424.0...@i3g2000cwc.googlegroups.com>:
Not from the excitement of solving a maths problem, no.