# Geometry

posted by
**John**
.

Let S be the set of {(1,1),(1,−1),(−1,1)} -lattice path which begin at (1,1) , do not use the same vertex twice, and never touch either the x -axis or the y -axis. Determine the largest value of n such that every path in S which ends at (n,n) has length at most 50000 .