Looking at the list of $w$ and $y$ values that must match up left-to-right, we have $(w,y) = A(4,6), B(1,3), C(3,5), D(7,4), E(9,7)$. Looking for digits that only appear once, we see that $9$, $6$, $1$, and $5$ cannot match up to other digits, and thus must appear on the ends. $1$ and $9$ only appear on the left, and thus their respective blocks $B$ and $E$ must appear on the left. Similarly, $6$ and $5$ only appear on the right, and thus their blocks $A$ and $C$ must appear on the right-most block of their row. Therefore, $D$, the only block without a unique digit, must be the top-center block.
Now that we have placed one block, $D$, we can only place block $E$ to the left of $D$, and block $A$ to the right of $D$. Thus, $\boxed{E}$ is the right answer.
Completing the puzzle, the top boxes read $EDA$, while the bottom two boxes read $BC$.