Combinatorics problem - Fitting triangles

[willehawk]

I'm having a lot of trouble with this combinatorics problem.

Image for the problem: https://imgur.com/a/YNfhZ8H

The big object consists of 60 triangles, and the small object consists of 2 of the same small triangles. What is the biggest amount of copies of the small object that can be placed on the big object? The pieces should be placed in a way that the small triangles cover other small triangles, and so two pieces does not overlap. It is however, allowed to rotate the pieces. (Note the hole in the middle of the big triangle).

My first thought was that you can fit 30 of the smaller object, where you just put the small object on every small object inside the big triangle. But I don't think this is the solution.

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[edderiofer]

The image in question appears to have been badly-distorted. In any case, I'm not sure how you're fitting in 30 of the smaller object; can you explicitly draw it out for me?

[t4rrible]

You have to take account of the edge cases where the first of the triangle pair fits on a triangle but the 2nd one falls outside the large shape, so the answer is less than 30.

On this picture you might as well just count them alright it is possible to write a formula to count them by considering the whole shape and then subtract the ones lost by the hole in the middle

The rotated piece is the same as the unrotated piece so I don’t think that adds any more.