A construction of a board
Source: Cono Sur 1997, Problem 4
May 11, 2018
cono surcombinatorics
Problem Statement
Consider a board with rows and columns. In the first line are written zeros (one in each house). Next, each line is then obtained from the previous line by performing the following operation: one of the houses, (that you can choose), is maintained as in the previous line; the other three are changed:
* if in the previous line there was a , then in the down square is placed;
* if in the previous line there was a , then in the down square is placed;
* if in the previous line there was a , then in the down square is placed;
Build the largest possible board with all its distinct lines and demonstrate that it is impossible to build a larger board.