Question

In the following, find the digits represented by the letters:
$1AA$
$\underset{–}{+1AA}$
$\underset{–}{2AA}$

Answer 1

In the given problem, the addition of $A$ with $A$ itself gives a number whose ones digit is $A$ again. This happens only when $A=0$. In the next step, the same will be done that is:

$A+A=A\Rightarrow 0+0=0$

In the last step, it is given that $1+1=2$ and therefore, the required sum with $A=0$ is $100+100=200$

Hence, the letter $A=0$.