MathDB

4

Part of 1994 Austrian-Polish Competition

Problems(1)

assigned number =|i - j | when endpoints of side are P_i,P_j

Source: Austrian - Polish 1994 APMC

5/3/2020
The vertices of a regular n+1n + 1-gon are denoted by P0,P1,...,PnP_0,P_1,...,P_n in some order (n≥2n \ge 2). Each side of the polygon is assigned a natural number as follows: if the endpoints of the side are PiP_i and PjP_j, then the assigned number equals ∣i−j∣|i - j |. Let S be the sum of all n+1n + 1 assigned numbers. (a) Given nn, what is the smallest possible value of SS? (b) If P0P_0 is fixed, how many different assignments are there for which SS attains the smallest value?
combinatoricspolygon