Philosopher's Chess
Source: Iran TST 2013-First exam-2nd day-P4
April 19, 2013
analytic geometrymodular arithmeticgeometryparallelogramvectornumber theorycombinatorics proposed
Problem Statement
and are two nonnegative integers. In the Philosopher's Chess, The chessboard is an infinite grid of identical regular hexagons and a new piece named the Donkey moves on it as follows:Starting from one of the hexagons, the Donkey moves cells in one of the directions, then it turns degrees clockwise and after that moves cells in this new direction until it reaches it's final cell.At most how many cells are in the Philosopher's chessboard such that one cannot go from anyone of them to the other with a finite number of movements of the Donkey?Proposed by Shayan Dashmiz