vipulgoyal wrote:I have a little query here "i" should be Precisely defined as function else i could also be 5! and in that case entire solution will be differ

I'm not sure exactly what you're asking, but I think you're wondering if the language of "i" signifies a function generally.

In this question, it's not actually a lowercase "i" but rather an upside-down exclamation point (!). Funny story... this question actually stemmed from a dream I had! I dreamed that I was doing factorial problems, and came across a "Spanish factorial" (in Spanish, an exclamation begins with an inverted exclamation point, and ends with a rightside-up one). In my dream, I wasn't sure how to solve the problem... because "Spanish factorials" don't actually exist! I told my coworkers about the dream, we all laughed about it, and this problem was the result.

I don't know if that actually helps to answer your question, but the larger idea is that whenever we're given function language, we want to apply the same definition given to the new circumstance.

In this case, ¡n! = 1*2*...*(n - 1)*n*n*(n - 1)*...*1. We just need to follow that definition for 17 and 16, as TheCode did correctly.