# What is so special about $$111$$ ?

Consider a regular $$111$$ sided polygon. We will get a decagon by joining any $$10$$ points of this $$111$$ sided polygon.

In this polygon, how many decagon can be formed such that they do not have any side common with the $$111$$ sided polygon?

If the answer contains $$m$$ digits and sum of all digits of the answer is $$n$$, find $$m + n$$.

$$\text{Details and Assumptions :}$$

$$\bullet$$ Sum of digits means sum of every individual digits. For example, sum of digits in number $$122453$$ is $$1+2+2+4+5+3 = 17$$

$$\bullet$$ You may use computational tools

×