MathDB

Let

n

be a positive integer. There are

\tfrac{n(n+1)}{2}

marks, each with a black side and a white side, arranged into an equilateral triangle, with the biggest row containing

n

marks. Initially, each mark has the black side up. An operation is to choose a line parallel to the sides of the triangle, and flipping all the marks on that line. A configuration is called admissible if it can be obtained from the initial configuration by performing a finite number of operations. For each admissible configuration

C

, let

f(C)

denote the smallest number of operations required to obtain

C

from the initial configuration. Find the maximum value of

f(C)

, where

C

varies over all admissible configurations.

Problem Statement