Question 1
A $21\times21$ square grid is shown. Each cell contains either $1$ or $-1$. Let $d_i$ be the product of the entries in row $i$, and let $c_j$ be the product of the entries in column $j$, for $i,j\in\{1,2,\ldots,21\}$. Set $D=d_1+d_2+\cdots+d_{21}$ and $C=c_1+c_2+\cdots+c_{21}$. Prove that $D+C\ne0$.
