Given two natural numbers a<b, Xavier and Ze play the following game. First, Xavier writes a consecutive numbers of his choice; then, repeat some of them, also of his choice, until he has b numbers, with the condition that the sum of the b numbers written is an even number. Ze wins the game if he manages to separate the numbers into two groups with the same amount. Otherwise, Xavier wins. For example, for a=4 and b=7, if Xavier wrote the numbers 3,4,5,6,3,3,4, Ze could win, separating these numbers into groups 3,3,4,4 and 3,5,6. For what values of a and b can Xavier guarantee victory? combinatoricsgame strategy