MathDB

5

Part of 1997 APMO

Problems(1)

N people passing objects

Source: APMO 1997

3/17/2006
Suppose that nn people A1A_1, A2A_2, …\ldots, AnA_n, (n≥3n \geq 3) are seated in a circle and that AiA_i has aia_i objects such that a1+a2+⋯+an=nN a_1 + a_2 + \cdots + a_n = nN where NN is a positive integer. In order that each person has the same number of objects, each person AiA_i is to give or to receive a certain number of objects to or from its two neighbours Ai−1A_{i-1} and Ai+1A_{i+1}. (Here An+1A_{n+1} means A1A_1 and AnA_n means A0A_0.) How should this redistribution be performed so that the total number of objects transferred is minimum?
algorithmrotationgeometrygeometric transformationlogarithmscombinatorics