Question 70
Find the smallest possible value of the expression
$$
\left\lfloor\frac{a+b+c}{d}\right\rfloor+\left\lfloor\frac{b+c+d}{a}\right\rfloor+\left\lfloor\frac{c+d+a}{b}\right\rfloor+\left\lfloor\frac{d+a+b}{c}\right\rfloor,
$$
in which $a$, $b$, $c$ and $d$ vary over the set of positive integers.
(Here $\lfloor x\rfloor$ denotes the biggest integer which is smaller than or equal to $x$.)
$$
\left\lfloor\frac{a+b+c}{d}\right\rfloor+\left\lfloor\frac{b+c+d}{a}\right\rfloor+\left\lfloor\frac{c+d+a}{b}\right\rfloor+\left\lfloor\frac{d+a+b}{c}\right\rfloor,
$$
in which $a$, $b$, $c$ and $d$ vary over the set of positive integers.
(Here $\lfloor x\rfloor$ denotes the biggest integer which is smaller than or equal to $x$.)