Thursday, September 22, 2005

power of 9

I learned a nifty, i mean really NIFTY trick in accounting class last night. ohh.. and by the way, kev, I got new respect for your 'business' degree. this accounting stuff is crazy! I thought senior engineering class was hard, these acocuntants go to EXTREME measures of 1940's style book keeping to keep from using a negative sign. and i'm not just talking aobut using parenthesis to designate negative, i'm talking about these guys hate negative!

ok..... have you guys heard of the divisible by 9 trick? turns out if you are summing two columns and the numbers dont' equal, if the difference is evenly divisble by 9, then you transposed some numbers.

I know you can't officially prove anything by example, but i'll give you an example
123 213
34 34
56 56
77 77
-- --
290 380

90/9 = 10

I played around with it a bunch in class and i can't quite figure out why it works. jen, see if you can puts your sets class to work and prove it for us!

yup topology was useful because it taught me to write better proofs. =) click on the image to see the full proof (a simple one and a generalized on that shows any two numbers switched, they don't have to be adjacent). sorry 'bout the quality... is a really nice pdf, but didn't take the time to convert to a higher quality png or something, just used print screen.
Free Image Hosting at


palegreenhorse said...

added two proofs to the post for any curious nerds.
the first is readily understandable but isn't a rigorous proof. the second is a generalized proof that is a bit more in depth.

palegreenhorse said...

oh ya... the complicated proof shows that you can also learn two more things by dividing by 9 that will help you find your transposition error. can anyone figure out what else you can know?

k2h said...

great work jen, thanks!

palegreenhorse said...

to download the much prettier pdf click here document.pdf

forkev said...

i'm feeling like less of a nerd everday after reading that!
on the otherhand, i got 60$ out of someone coming to visit for 1.5 hours. turns out they like my ideas. i told them more ideas were availble, but me doing the developement was NOT.