Problem

Source: Iranian TST 2018, second exam day 1, problem 2

Tags: combinatorics, Iran, Iranian TST, game strategy, game, Game Theory



Mojtaba and Hooman are playing a game. Initially Mojtaba draws $2018$ vectors with zero sum. Then in each turn, starting with Mojtaba, the player takes a vector and puts it on the plane. After the first move, the players must put their vector next to the previous vector (the beginning of the vector must lie on the end of the previous vector). At last, there will be a closed polygon. If this polygon is not self-intersecting, Mojtaba wins. Otherwise Hooman. Who has the winning strategy? Proposed by Mahyar Sefidgaran, Jafar Namdar