sqing wrote: Let $x,y,z \in [0,1]$ , and $|y-z|\leq \frac{1}{2},|z-x|\leq \frac{1}{2},|x-y|\leq \frac{1}{2}$ . Find the maximum and minimum value of $W=x+y+z-yz-zx-xy$. hello, we get \[0\le W\le \frac{5}{6}\] the minimum holds if $x=y=z=0$ and the maximum holds if $x=2/3,y=1/6,z=2/3$ Sonnhard.