## Problem of the Day #114: Digits in Triangles
*July 11, 2011*

*Posted by Arjun in : potd , trackback*

$x$ and $y$ are positive four-digit integers whose digits can be taken from the set of positive integers less than $7$. If $z$ is the maximum possible integer side length of a triangle with sides $x$, $y$, and $z$, find the sum of all $z$ for all $x$ and $y$.

## Comments»

clarification request: should we count z=2222 twice for x=1111 y=1112 and x=1112 y=1111?

yes, count it twice; it’s for all x and y.