2023 Fermat Problem 16

Twenty-five cards are randomly arranged in a grid, as shown. Five of these cards have a 0 on one side and a 1 on the other side. The remaining twenty cards either have a 0 on both sides or a 1 on both sides. Loron chooses one row or one column and flips over each of the five cards in that row or column, leaving the rest of the cards untouched. After this operation, Loron determines the ratio of 0s to 1s facing upwards. No matter which row or column Loron chooses, it is *not possible* for this ratio to be

\begin{array}{|c|c|c|c|c|}\hline 0 & 0 & 1 & 1 & 0 \\ \hline 1 & 0 & 0 & 1 & 0 \\ \hline 1 & 1 & 0 & 1 & 0 \\ \hline 0 & 0 & 1 & 0 & 0 \\ \hline 1 & 0 & 1 & 0 & 1 \\ \hline \end{array}

\textbf{(A)}\ 12 : 13\quad \textbf{(B)}\ 2 : 3\quad \textbf{(C)}\ 9 : 16\quad \textbf{(D)}\ 3 : 2\quad \textbf{(E)}\ 16 : 9

If there are no answer choices shown, enter a numerical answer.

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