2008 AIME II Problem 9

A particle is located on the coordinate plane at (5,0). Define a *move* for the particle as a counterclockwise rotation of \pi/4 radians about the origin followed by a translation of 10 units in the positive x-direction. Given that the particle's position after 150 moves is (p,q), find the greatest integer less than or equal to |p| + |q|.

Leading zeroes must be inputted, so if your answer is 34, then input 034

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.