[DeTomaso] NPC Whatsoever: Mind Game

[Trevor Fougere]

The proof is fairly simple
 
any two digit number can be expressed as (10X + Y) where X, Y are elements
of the set (0-9)
 
adding the two digits together gives you (X + Y)
 
so     (10X + Y) -  ( X + Y)  =     10X + Y - X - Y
 
which = 10X - X + Y - Y
 
which = 10X - X + 0
 
which =  9X + 0
 
which = 9X 
 
hence all are divisible by 9
 
 
Inerestingly is works for three digit numbers as well....briefly
 
100X + 10Y + Z - X - Y - Z = 99X + 9Y = 9 ( 11X + Y) = hence divisible by 9
 
Oh
 
and it works for 4 digit numbers ....5 digit numbers..
 
the proofs remain elemental as previously describe...
 
I leave the proof for all positive integers greater than or equal to 10 to
the reader.....
 
 
Trevor "IL CONTE" and back on the road again...