Question 83
A game is played on a regular triangle which is split into $n^2$ equal smaller regular triangles by lines that are parallel to one of the sides of the triangle. Denote a "line of triangles" to be all triangles that are placed between two adjacent parallel lines that forms the grid.
In the beginning of the game all triangles are white. At each move one line of triangles that contains at least one white triangle is colored black. Situation with $n=6$ after possible 4 moves is shown in Figure 1. The game ends when all triangles are colored black. Find the smallest and largest possible number of moves in the game.
Figure 1
In the beginning of the game all triangles are white. At each move one line of triangles that contains at least one white triangle is colored black. Situation with $n=6$ after possible 4 moves is shown in Figure 1. The game ends when all triangles are colored black. Find the smallest and largest possible number of moves in the game.
Figure 1