BdMO Online Forum

The problem statement assures that the aliens use $12$ based number system.So we can covert this in the way how we convert decimal to binary or octal or hexa and so on.First we can make a chart:
Decimal -> Aliens($12$ based)

• $ 0 -> 0$
  $ 1 -> 1$
  $ 2 -> 2$
  $ 3 -> 3$
  $ 4 -> 4$
  $ 5 -> a$
  $ 6 -> 5$
  $ 7 -> 6$
  $ 8 -> 7$
  $ 9 -> 8$
  $ 10 -> 9$
  $ 11 -> b$

So $1b = 1*(12^1) + 11*(12^0) = 12 + 11 = 23$
So $(1b)^2 = 23^2 = 529$
Now convert it into 12 based system as you convert decimal to binary.Instead of dividing by $2$ divide by $12$.
Convert the remainders according to the chart.For example:If you get a remainder $5$ replace it by $a$ .
If you do this correctly you will get the answer $371$.