$\textbf{Multiplication}$
In the multiplication problem below, $A$, $B$, $C$, and $D$ are different digits. What is $A+B$? $$\begin{array}{cccc}& A & B & A\\ \times & & C & D\\ \hline C & D & C & D\\ \end{array}$$
$\textbf{Answer}$
$1$
$\textbf{Analysis}$
Of course it is possible to use the trial and error approach to determine the value of all these letters. However, there is a quick way by noting the identity $$CD\cdot 101 = CDCD$$
Therefore, $ABA = 101 \implies A+B =1$.
$\textbf{Note}$
Most brain teasers do not require math knowledge. However, sometimes, having some math knowledge can be very helpful.