Thank you and yes I understood it enough to solve the problem now. Super cool!

Thank you for the diagram of the 12th hexagon. As soon as you posted it the solution you were looking for presented itself to me, and ultimately led to the slightest change in my formula. Amazing that the formulas could be so close and yet so far from each other! I really like this and it's the second time I've managed to solve a 6kyu problem!

Added. Hope this will be understandable

Maybe adding this to the description :

<svg xmlns:osb="http://www.openswatchbook.org/uri/2009/osb" xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 127.219 110.614" height="418.069" width="480.829"><defs><linearGradient osb:paint="solid" id="a"><stop offset="0" stop-color="#00df00"/></linearGradient><linearGradient gradientUnits="userSpaceOnUse" y2="150.473" x2="118.61" y1="150.473" x1="55.382" id="b" xlink:href="#a"/></defs><path d="M93.458 89.647l-29.595 16.91-29.442-17.175.153-34.085 29.595-16.91L93.61 55.562z" fill="#00f8fc" stroke="#000" stroke-width=".185"/><path transform="matrix(.93938 -.55445 .54937 .94807 -100.327 -22.187)" d="M118.349 168.762l-31.515 18.007L55.48 168.48l.163-36.296 31.515-18.008 31.352 18.29z" fill="none" stroke="url(#b)" stroke-width=".197"/><path d="M123.851 106.281l-118.882.821L63.699 3.737z" fill="none" stroke="#ed0000" stroke-width=".338"/></svg>

Already have in description:

Let H(n) be the number of all regular hexagons that can be found by connecting 6 of these points.

I think a more helpful tip is to stress that the hexagons are formed by points and not lines.

@vlukyanets: just say it in the description (that the hexagons can have different orientations) otherwise you'll get hundreds of messages asking for this.

Searching 12th hexagon is way to solution

i also encountered the same issue, and i can't submit my attempt
although im 100% sure it's good
formula in reply (SPOILER)
btw, what formula is the tester using?

I'm working on this problem and I can't figure out how there are 12 hexagons in n=6 triangle. I count 10 if we only include length 1 hexagons, and 11 if we include the larger (length = 2) hexagon. I have a formula for finding hexagons with length 1 and also have a formula which I believe solves for all hexagon sizes. Am I missing something obvious? (I drew the triangle and counted the hexagons just to be sure).

To be honest, I hadn't any other ideas and i was struggling with this for a while. I'm shocked how other people can do this task with only two or three lines of code.
Thank you btw :-D

I'm glad I didn't know this existed.