BALIFE help with logic

#1

I am not able to crack the logicof this question. can you please help me with the logic.

#2

Careful observation here is that you decrease a particular element by 1 and add 1 to any adjacent neighbours(if it exists,eg A[0] has only one neighbour which is A[1]), so this way your sum of all elements is constant. Now for all elements to be equal, the average of given elements should be integer(example for N=3,A= (1,1,2 )has no possible answer as average is 4/3 which is not an integer). Now if average is integer, think upon making each element equal to this average.