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

 

[quicknote]

Hi there,

It seems like you are on the right track with your approach to solving this puzzle. However, there are a couple of things that need to be clarified.

First, it is not necessary for M to equal 1. In fact, it can be any number from 0-9. This is because the value of M does not affect the outcome of the addition. For example, if M = 2, the equation would be:

.. S E N D
+ M O R E
---------
M O N E Y

This would still result in the same values for S, E, N, D, O, R, and Y.

Second, your reasoning for S = 9 is correct. However, your reasoning for R = 9 is incorrect. Remember, the goal is for each letter to represent a different digit. Therefore, R cannot be equal to 9 because S is already equal to 9. So, you must find a different value for R that still satisfies the equation.

One approach you can take is to start by assigning values to the letters that have the most restrictions. In this case, it would be O and S. From your work, we know that S = 9 and O = 0. Now, let's look at the carryover values in the equation:

.. 9 E N D
+ 0 0 R E
---------
0 N E Y

Since O = 0, there is no carryover value from the ones place. This means that the carried value from the tens place must be 1. This carried value can only come from the sum of E + R + 1. So, E + R must be equal to 9 (since we already know that S = 9). This means that the possible values for E and R are 4 and 5, or 5 and 4.

Let's try both possibilities:

1) If E = 4 and R = 5, the equation would be:

.. 9 4 N D
+ 0 0 5 4
-----------
0 N 4 Y

From here, we can see that N = 5 (since there is a carryover from the ones place) and D = 6 (since 4 + 5 = 9). However, this creates a problem with the value of Y. Since N = 5, Y must be equal to 0