Triangular grid divides an equilateral triangle with sides of length n into n2 triangular cells as shown in figure for n=12. Some cells are infected. A cell that is not yet infected, ia infected when it shares adjacent sides with at least two already infected cells. Specify for n=12, the least number of infected cells at the start in which it is possible that over time they will infected all the cells of the original triangle. [asy][asy] unitsize(0.25cm); path p=polygon(3); for(int m=0; m<=11;++m){ for(int n=0 ; n<= 11-m; ++n){ draw(shift((n+0.5*m)*sqrt(3),1.5*m)*p); } } [/asy][/asy]
Problem
Source: Czech - Polish - Slovak Match 2013: P5
Tags: geometry, perimeter, inequalities, combinatorics unsolved, combinatorics