# Why is this 24 on AMC 10?

Algebra Level pending

Aaron the ant walks on the coordinate plane according to the following rules. He starts at the origin p0 = (0,0) facing to the east and walks one unit, arriving at p1=(1,0). For n=1,2,3,... right after arriving at the point pn, if Aaron can turn 90 degrees left and walk one unit to an unvisited point p{n+1}, he does that. Otherwise, he walks one unit straight ahead to reach p{n+1}. Thus the sequence of points continues p2=(1,1), p3=(0,1), p4=(-1,1), p5=(-1,0) and so on in a counterclockwise spiral pattern. p{2015}'s coordinates can be expressed as (a,b). Find the absolute value of 3a-b. Source: AMC 10

×