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Is it subjective on which is better, or is it something objective by codeforces?

Whenever I start counting the CF Tags I know one by one, Geometry Always comes almost the last, I think it is very unpopular on CF aswell.

Geometry problems, add more geometry problems

I have seen a lot of great adhoc ideas be used in several topics and tags, but geometry and some others occurred very rare, I think trying to take advantage of such uncommon ideas may help in getting ideas for problems.

I have noticed though that in the early years of codeforces some really good geometry problems were proposed, I think it will be cool to revive this era.

Define a function $$$s(n)$$$ (where $$$n$$$ is an integer) which returns the successor of the integer $$$n$$$

Define another function $$$f(a,b,k)$$$ such that $$${a,b,k}$$$ belong to integers, $$$f(a,b,0)$$$ = $$$s(s(s(.....s(s(a))......)))$$$ **(call function $$$f$$$ on $$$a$$$ for $$$b$$$ times)**, and $$$f(a,b,k)$$$ = $$$f(a,f(a,f(a,.......f(a,f(a,b,k-1),k-1),k-1),......),k-1)$$$ **(call function f such that the second parameter b is this function nested b-1 times and the third parameter is k-1)**

It can be shown that $$$f(a,b,0)$$$ = $$$a+b$$$, $$$f(a,b,1)$$$ = $$$a*b$$$, $$$f(a,b,2)$$$ = $$$a^b$$$, and $$$f(a,b,3)$$$ = $$$a↑↑b$$$ **(Tetration symbol)**

Any thoughts about this function and the best different complexities to calculate it in terms of $$$a,b,k$$$ in preprocessing and the call of this function?

You are given a hexagon in which all his angles are equal in measure, you draw a circle inscribed inside the hexagon and tangent to the hexagon's sides, and another circle which is the circumscribed circle of the hexagon (all the hexagon vertices lie on the circumference of this circle), suppose the side length of the hexagon is $$$X$$$, find the area of the ring between the two circles in terms of $$$X$$$.

**The ring in yellow is the required ring**

BONUS : Find a general solution in terms of $$$N$$$ and $$$X$$$ **(where polygon $$$P$$$ is a regular $$$N$$$th-gon of side length $$$X$$$ each)** for the area of the ring between the circle inscribed in $$$P$$$ and the circle $$$P$$$ is inscribed in

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