Is there some reasonable way to divide an even number of variables with an even range to odd output variable ranges?

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Is there some reasonable way to divide an even number of variables with an even range to odd output variable ranges?

Such as:

$$y=f(a_1,a_2,a_3,a_4)$$

$a_1,a_2,a_3,a_4 \in [0,2]$ and equally weighted.

And we want that the function produces the range $[0,8]$ (e.g. if the model is $a_1+a_2+a_3+a_4$) to:

$y \in \{1,2,3\}$.

The rough idea would be to divide the range $[0,8]$ of $f(a_1,a_2,a_3,a_4)$ by $3$, but this produces a bit ugly 2.66666666667.

Compared to if we had $a_1+a_2+a_3$ and we could do $6/3=2$ so that the mappings would be $[0,2]\rightarrow 1, [2,4] \rightarrow 2, [4,6] \rightarrow 3$.