Solve the following system of equations:

$$
\begin{aligned}
& x+[y]+\{z\}=1.1 \\
& \{x\}+y+[z]=2.2 \\
& {[x]+\{y\}+z=3.3}
\end{aligned}
$$

where $[x]$ denotes the greatest integer not greater than $x$, and $\{x\}=x-[x]$.
Adding up the three equations and dividing by two, we arrive at the following equation:

$$
x+y+z=3.3 \text {. }
$$

Subtracting each of the original system of equations from this, we get the following equations:

$$
\begin{aligned}
& \{y\}+[z]=2.2 \\
& {[x]+\{z\}=1.1} \\
& \{x\}+[y]=0 .
\end{aligned}
$$

From these equations, using the interpretation of fractional and integer parts, it directly follows that

$$
\begin{aligned}
& {[x]=1, \quad\{x\}=0} \\
& {[y]=0, \quad\{y\}=0.2} \\
& {[z]=2, \quad\{z\}=0.1}
\end{aligned}
$$

Thus, \( x=1, y=0.2 \) and \( z=2.1 \).

Substitution can verify that this triplet indeed satisfies the system of equations.