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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»

1. phenomist - July 11, 2011

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

2. Arjun - July 11, 2011

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