Question

In the following, find the digits represented by the letters:
$2A$
$\underset{–}{\times A}$
$\underset{–}{12A}$

Answer 1

In the given problem, the multiplication of $A$ with $A$ itself gives a number whose ones digit is $A$ again. This happens only when $A=1,5,6$.

If $A=1$ then the multiplication will be $21\times 1=21$. However, here the tens digit is given as $12$, therefore, $A=1$ is not possible.

Similarly if $A=5$ then the multiplication will be $25\times 5=125$, therefore, $A=5$ is possible.

Hence, the letter $A=5$.