MathDB

Consider a board with

n

rows and

4

columns. In the first line are written

4

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

0

, then in the down square

1

is placed; * if in the previous line there was a

1

, then in the down square

2

is placed; * if in the previous line there was a

2

, then in the down square

0

is placed; Build the largest possible board with all its distinct lines and demonstrate that it is impossible to build a larger board.

4

Problems(1)