Question 18
There is a rectangular board of $5 \times 50$, divided into squares of $1 \times 1$, and dominoes of $1 \times 2$, each with two numbers written on it: a $1$ and a $-1$, one in each half. Each domino covers exactly two neighboring squares on the board. Gabriel must cover the board with these pieces, without gaps or overlaps, and in such a way that in each row of the board the multiplication of the $50$ numbers is positive, and in each column of the board the multiplication of the $5$ numbers is positive.
Decide if Gabriel can make it. What if the board is from $5 \times 100$?
If yes, indicate how the board is covered. If not, explain why.
Decide if Gabriel can make it. What if the board is from $5 \times 100$?
If yes, indicate how the board is covered. If not, explain why.