Question 5
Suppose $n\ge3$ people $A_1,\ldots,A_n$ sit in a circle, and $A_i$ has $a_i$ objects, with $a_1+\cdots+a_n=nN$ for a positive integer $N$. To give everyone the same number of objects, each $A_i$ may give objects to or receive objects from the neighbors $A_{i-1},A_{i+1}$, with cyclic indices. How should redistribution be performed to minimize the total number of objects transferred?