Given that $x$, $\frac{1}{x}$, $y$, $\frac{1}{y}$, $z$ and $\frac{1}{z}$ are all integers, how many distinct values of $x+ y+ z$ are possible?
+37157 I think x y and z can each be 1 or -1
1 + 1 +1 = 3
-1 + 1 +1 =1
-1 -1 + 1 = -1
-1 -1 -1 = -3 4 values
