### Theory:

Like how dealing with numbers could be a fascinating experience, the mix of numbers and the alphabet letters could also be equally fascinating.

Let us consider the following puzzle.

Instructions:

1. Each of the letters of the alphabet will only constitute one-digit.

2. The first digit of a number can never be '$$0$$'.

Let us try to solve the following puzzle.

In this puzzle, we should try to find the value of $$A$$.

Let us consider the entries in the ONES column.

$$A + 4 = 1$$

It is now understood that $$A$$, when added with $$4$$, gives a number ending with $$1$$.

What are the numbers that end with $$1$$?

$$1$$, $$11$$, $$21$$, $$31$$,$$...$$

Let us look at the trial and error method:

 Variable$$A$$ Operation$$A + 4$$ Final answer $$0$$ $$0 + 4$$ $$4$$ $$1$$ $$1 + 4$$ $$5$$ $$2$$ $$2 + 4$$ $$6$$ $$3$$ $$3 + 4$$ $$7$$ $$4$$ $$4 + 4$$ $$8$$ $$5$$ $$5 + 4$$ $$9$$ $$6$$ $$6 + 4$$ $$10$$ $$7$$ $$7 + 4$$ $$11$$

When we consider $$A$$ as $$7$$, the final value is a number ending with $$1$$.

Let us consider the HUNDREDS column.

$$1 + A = 8$$

Let us check if the condition $$A = 7$$ is satisfied or not.

$$1 + 7 = 8$$

The condition is thus satisfied.

If we substitute $$7$$ in the place of $$A$$, we get the following.

This type of puzzle solving is called 'Cracking of codes' or 'Cryptarithms'.