Let's suppose that $\{a, b, c\}$ are distinct integers between $1$ and $9$. If we consider two real numbers with decimal representation $a,b$ and $c,b$ that sum up to an even integer, which of the expressions among $a+b+c$, $(a+c)c$, $ac+b$, or $(a+b)c$, and $abc$ can be argued certainly to be even or odd?
For $a,b+c,b = (a+\frac{b}{5})+(c+\frac{b}{10}) = (a+c)+\frac{2b}{10}$ to be an integer, one demands that $\frac{2b}{10}\in \mathbb{Z}$ which requires $2b = 10$ and $b = 5$.
$$a+c+1\equiv 0\pmod{2}\rightarrow a\equiv 1+c\pmod{2}$$
From which it holds immediately $a+b+c = a+c+5$ is even.
$$(a+c)c\equiv (1+2c)c \equiv c\pmod{2}$$
Which depends on $c$ being even or odd.
$$ac+b = ac+5\equiv (1+c)c+1 = c^2+c+1\pmod{2}$$
Which is always odd regardless of what $c$ is.
$$(a+b)c\equiv (c+2)c\equiv c^2\pmod{2}$$
Which depends on $c$ being even or odd.
$$abc = 5ac\equiv ac\equiv (1+c)c = c^2+c\pmod{2}$$
Which is always even regardless of what $c$ is.