n points, vectors, 2 player game - All-Russian MO 2002 Regional (R4) 11.6
Source:
September 17, 2024
vectorcombinatoricscombinatorial geometry
Problem Statement
There are points on the plane. Two take turns connecting more an unconnected pair of points by a vector of one of two possible directions. If after the next move of a player the sum of all drawn vectors is zero, then the second one wins; if it's another move is impossible, and there was no zero sum, then the first one wins. Who wins when played correctly?