Question 48
On a board in the shape of an equilateral triangle with an even number of rows $n$ (as indicated in the figure), solitaire is played.
A token is placed on each square. Each token is white on one side and black on the other. Initially, only one tile, which is located at a vertex, has the black side facing up; The other pieces have the white side facing up. In each move of the game, only one black piece is removed from the board and each of the pieces occupying a neighboring square is turned over. (Neighboring boxes are those that are joined by a segment.)
After several moves, will it be possible to remove all the pieces from the board?
A token is placed on each square. Each token is white on one side and black on the other. Initially, only one tile, which is located at a vertex, has the black side facing up; The other pieces have the white side facing up. In each move of the game, only one black piece is removed from the board and each of the pieces occupying a neighboring square is turned over. (Neighboring boxes are those that are joined by a segment.)
After several moves, will it be possible to remove all the pieces from the board?