Question

In the following, find the digits represented by the letters:
$3A$
$\underset{–}{\times A}$
$\underset{–}{2BA}$

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 $31\times 1=31$. However, here the tens digit is given as $B$ and hundred digit is $2$, therefore, $A=1$ is not possible.

Similarly, if $A=5$ then the multiplication will be $35\times 5=175$. However, here the tens digit is given as $B$ and hundred digit is $2$, therefore, $A=5$ is not possible.

Now, if $A=6$ then the multiplication will be $36\times 6=216$. However, here the tens digit is given as $B$ and hundred digit is $2$, therefore, $A=6$ and $B=1$ are possible.

Hence, the letter $A=6$ and $B=1$.