61 The number of real roots of the equation $x=\sin x+1993$ is
A. 0
B. 1
C. 2
D. Greater than 2
61 B. The root of the equation $x=\sin x+1993$ is the x-coordinate of the intersection point of the line
$$
y=x
$$

and the curve
$$
y=\sin x+1993
$$

Therefore, the equation has at least one real root.
Assume the equation has two real roots $x_{1}, x_{2}, x_{1} \neq x_{2}$, then we have
$$
x_{1}=\sin x_{1}+1993, \quad x_{2}=\sin x_{2}+1993 .
$$

Subtracting the two equations yields
$$
\begin{aligned}
\left|x_{1}-x_{2}\right| & =\left|\sin x_{1}-\sin x_{2}\right|=2 \cdot\left|\sin \frac{x_{1}-x_{2}}{2}\right| \cdot\left|\cos \frac{x_{1}+x_{2}}{2}\right| \\
& < 1 .
$$

This is clearly not true. Therefore, the original equation has only one real root.