Question 8
If $a, b, c \gt 0$, what is the smallest possible value of $\left\lfloor\frac{a+b}{c}\right\rfloor + \left\lfloor\frac{b+c}{a}\right\rfloor + \left\lfloor\frac{c+a}{b}\right\rfloor$? (Note that $\lfloor x \rfloor$ denotes the greatest integer less than or equal to $x$.)