Fun hw question I can't seem to get

[rocketboy]

Alright, this one has been bugging me for awhile now.

"In the following addition, each letter represents a different digit. Find the values of the letters."

.. S E N D periods are just there to push the "S E N D" over.
+ M O R E
---------
M O N E Y


Here's what I have so far:
1) M must = 1
2) Thus O must = 0, because S + M must generate a remainder, yet the numbers S and M can't add to more than 10 because M = 1, and even if there was a carried place value, it would add to 11 which can't be true because there can only be one 1 value.
3) Thus S = either 8 or 9; it can equal 8 if E + O generates a remainder, which it can only if E = 9. But since O = 0, N can't also be 0, so I decided that it can't generate a remainder, and thus S = 9. (Sorry for the ambiguous wording there.)
4)Since E can't = N, and since O = 0, the N + R has to produce a remainder so that the carried place value can be added to E (in the E + O = N column) to make the result of N different from E.

Somehow whenever I work it out, I always get R to equal 9, but it can't because that is what S is equal to. AAAAAAHHHH.

Am I on the right track? I MUST have done something wrong.

 

[rocketboy]

HAHAHAH I AM VICTORIOUS!

If you want the answer highlight below this text, but not if you are so into the question and want to figure it out yourself! (It's very rewarding when you do).

9567 + 1085 = 10652