Let some finite array of integers is given initially.There is a number k which is initially '0'.In a move, a player will select a number from the array arr[i] and change k to gcd(k,arr[i]).Also, the number chosen from the array(i.e a[i]) will be removed from that array.CONSTRAINTSA player who makes k=1 at any step loses.A player who cannot move also loses.2 players are playing the game optimally.When will the player who moves first wins the game?
What is the optimal strategy for this 2 player game?
ds.algorithms;pr.probability;gt.game theory;combinatorial game theory