In the addition shown, each letter represents a different digit ranging from zero to nine. It is already known that
$$
S=9, O=\text { zero, } E=5 \text {. }
$$

Find the numbers represented by
(i) $M$,
(ii) $N$,
(iii) $R$,
(iv) $Y$
Consider the thousands digit and the ten thousands digits.
$$
0 \leq S, M \leq 9,9+M=10 M+0 \text { or } 9+M+1=10 M+0
$$
$\Rightarrow M=1$ and there is no carry digit.
Consider the hundreds digit. $5+0+1=N$
$\Rightarrow N=6$ and there is a carry digit.
For the tens digit. $6+R=10+5$
$$
\begin{array}{l}
\Rightarrow R=9 \text { (same as } S, \text { rejected) or } 6+R+1=10+5 \\
\Rightarrow R=8
\end{array}
$$

There is a carry digit in the unit digit
$$
\begin{array}{l}
D+5=10+Y,(D, Y)=(7,2) \Rightarrow Y=2 \\
\therefore M=1, N=6, R=8, Y=2
\end{array}
$$