MathDB

On each side of an equilateral triangle with side length

n

units, where

n

is an integer,

1 \leq n \leq 100

, consider

n-1

points that divide the side into

n

equal segments. Through these points, draw lines parallel to the sides of the triangle, obtaining a net of equilateral triangles of side length one unit. On each of the vertices of these small triangles, place a coin head up. Two coins are said to be adjacent if the distance between them is 1 unit. A move consists of flipping over any three mutually adjacent coins. Find the number of values of

n

for which it is possible to turn all coins tail up after a finite number of moves.

Problem Statement