Problem

Source: Iran third round combinatorics problem 1

Tags: combinatorics



Alice and Bob are play a game in a $(2n)*(2n)$ chess boared.Alice starts from the top right point moving 1 unit in every turn.Bob starts from the down left square and does the same.The goal of Alice is to make a closed shape ending in its start position and cannot reach any point that was reached before by any of players .if a players cannot move the other player keeps moving.what is the maximum are of the shape that the first player can build with every strategy of second player.