If ABC+DEF+GHI=JJJ, each letter stands for a different digit, and no number starts with zero, what is J?
"casting out nines" is a process used to find the remainder of an integer when divided by nine. It is the same as the what Charlie calls the "digital root", except that a "digital root" of 9 equals a remainder of 0.
At any rate, add J to each side of this equation.
Then the left side (which contains the disits 0 through 9) divides evenly by 9 (by "casting out nines"), so the the right side JJJ + J has to divide evenly by 9 also. JJJ + J has the same remainder as 4*J when divided by 9, so J must be 0 or 9.
But J clearly cannot be 0, so J = 9.
Edited on February 10, 2021, 7:07 am
Simpler method
