triangular cells of an equilateral triangle are infected
Source: Czech - Polish - Slovak Match 2013: P5
May 29, 2014
geometryperimeterinequalitiescombinatorics unsolvedcombinatorics
Problem Statement
Triangular grid divides an equilateral triangle with sides of length into triangular cells as shown in figure for . 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 , 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]
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]