2025 Gauss 8 Problem 21

In the diagram, each letter from A to H is equal to a different integer from 1 to 8. Also,

\begin{array}{|c|c|}\hline A & E \\ \hline B & F \\ \hline C & G \\ \hline D & H \\ \hline\end{array}

- H is a perfect square and is 1 more than D - 5\ \text{and} 8 are in the same row - C is a multiple of both G and D - B is the largest prime number in the set - The value of B + G is even

What is the value of F?

\textbf{(A)}\ 2\quad \textbf{(B)}\ 6\quad \textbf{(C)}\ 1\quad \textbf{(D)}\ 7\quad \textbf{(E)}\ 8

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

Full credit to this problem is given to the CEMC, you may view all Gauss contests here.