Particle with Interesting Movements
Source:
November 13, 2005
analytic geometry
Problem Statement
A particle moves in the Cartesian Plane according to the following rules:
1. From any lattice point , the particle may only move to (a \plus{} 1,b), (a,b \plus{} 1), or (a \plus{} 1,b \plus{} 1).
2. There are no right angle turns in the particle's path.
How many different paths can the particle take from to ?