In the classic alphametic equation $\text{SEND} + \text{MORE} = \text{MONEY}$, where distinct letters represent distinct decimal digits from $0$ to $9$ and $S \neq 0, M \neq 0$, what digit is represented by the letter $M$?
Options:
(A) $1$
(B) $2$
(C) $9$
(D) $0$
Answer Key:
A
Step-by-Step Solution & Explanation
**Method 1: Column-Wise Carry Deduction**
1. In the leftmost column, the sum of two 4-digit numbers $\text{SEND} + \text{MORE}$ produces a 5-digit number $\text{MONEY}$. The maximum possible sum of two single digits with a carry is $9 + 9 + 1 = 19$, meaning the highest possible carry-over to a new column is 1.
2. Since $M \neq 0$, $M$ must be $1$.
Option **A** is correct.