Question 40
A $1$ or a $-1$ is put into each cell of an $n \times n$ array as follows. A $-1$ is put into each of the cells around the perimeter. An unoccupied cell is then chosen arbitrarily. It is given the product of the four cells which are closest to it in each of the four directions. For example, if the cells below containing a number or letter (except $x$) are filled and we decide to fill $x$ next, then $x$ gets the product of $a$, $b$, $c$ and $d$.
- 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 a 1 -1 c x d -1 -1 -1 b -1 -1 -1 -1
What is the minimum and maximum number of $1$s that can be obtained?
- 1 -1 -1 -1 -1 -1 -1 -1 -1 -1 -1 a 1 -1 c x d -1 -1 -1 b -1 -1 -1 -1
What is the minimum and maximum number of $1$s that can be obtained?