smc

First, we can find out that the only $x,y,z$ that satisfy the conditions in the problem are $(1\le z-y\le 9,1\le y-x\le 9,z-x\ge 10)$ , $(1\le y-x\le 9,1\le x-z\le 9,y-z\ge 10)$ , and $(1\le x-z\le 9,1\le z-y\le 9,x-y\ge 10)$. Consider the 1st set of conditions for $x,y,z$. We get that there are $$45\cdot 10-\sum _{k=1}^9\left(\genfrac{}{}{0ex}{}{k+1}{2}\right)=285$$ cases for the first set of conditions. Since the 2nd and 3rd set of conditions are simply rotations of the 1st set, the total number of cases is $$3\cdot 285=\boxed{855}$$