i just realized some simple math

[kstu]

say you have a two digit number, AB, where A is the tens digit and B is the ones digit and another two digit number, CD, similar to AB, where CD = BA. for example, AB = 73 and CD = 37 (A = 7, B = 3, C = 3, D = 7).

AB - CD = 9 * (D - B)

works for any numbers.

examples:

81-18 = 9 * (8-1) = 63
97-79 = 9 * (9-7) = 18

is there theorem or something about this already that ive just forgotten since high school?

 

[ggavinmoss]

Alright tough guy, now prove it. And none of that weak induction sh!t either.

-geoff

 

[TuxDave]

Originally posted by: kstu
say you have a two digit number, AB, where A is the tens digit and B is the ones digit and another two digit number, CD, similar to AB, where CD = BA. for example, AB = 73 and CD = 37 (A = 7, B = 3, C = 3, D = 7).

AB - CD = 9 * (D - B)

works for any numbers.

examples:

81-18 = 9 * (8-1) = 63
97-79 = 9 * (9-7) = 18

is there theorem or something about this already that ive just forgotten since high school?

AB = 10A+B
CD = 10C+D
Since you said A=D and B=C

AB-CD=AB-BA= 10A+B-10B-A=9(A-B)=9(D-B)

 

[Legendary]

Anyone remember that crystal ball thing from a few months ago? It was based on this same principle.
To clarify, the crystal ball thing was where you'd pick a number, do some functions which resembled flipping the number around, and would always end up with a multiple of nine, which is what the ball would guess.