1990 AMC 8 Problem 10

On a calendar, moving one column right adds $1$ to the date and moving one row down adds $7$

The date behind $C$ is one less than the date behind $A$, so the missing date must be one more than the date behind $B$

Moving one column right adds $1$ to the date, and moving one row down adds $7$. Let $C$ have date $n$. Then $A$, one column to the right, is $n+1$. The letter $P$ sits two rows directly below $C$, so $P = n+14$, and $B$, one column left of $P$ in the bottom row, is $n+13$.

We need a letter whose date $d$ satisfies $d + n = (n+1) + (n+13)$, so $d = n + 14$. That date is behind $P$.

Thus, the correct answer is A .