Question 15
A $7 \times 7$ board has a lamp in each of its 49 cells, which can be on or off. The allowed operation is to choose 3 consecutive cells of a row or of a column that have two neighbouring lamps on and the other one off, and to change the state of all three. That is:
Give a configuration of exactly 8 lit lamps located in the first 4 rows of the board such that, through a sequence of allowed operations, one arrives at a single lit lamp on the board, located in the last row. Show the sequence of operations used to achieve the goal.
Give a configuration of exactly 8 lit lamps located in the first 4 rows of the board such that, through a sequence of allowed operations, one arrives at a single lit lamp on the board, located in the last row. Show the sequence of operations used to achieve the goal.