Count the number of triangles in the figure using permutation and combination

Question

mathmath333 · Answer

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mathmath333 · Answer

$\large \color{black}{\begin{align}
& \normalsize \text{Count the number of triangles in the figure using }\hspace{.33em}\~\
& \normalsize \text{ permutation and combination}\hspace{.33em}\~\
\end{align}}$

mathmath333 · Answer

answer is 28.

mathmate · Answer

I also got 28, but splitting it into permutations and combinations would be very messy!
Hope someone would enlighten us on this!

loser66 · Answer

*

mathmath333 · Answer

yes counting manually is very easy

mathmath333 · Answer

i doubt that there is a way P&C way

mathmate · Answer

The worry is if there are many panels in both dimensions, then it would be messy if we're not systematic.

chillout · Answer

I can only split in two cases - I can't fit the smallest triangles in a case where a formula applies. :(

mathmate · Answer

Yeah, then there are exterior and interior nodes, and the "invisible nodes" where the diagonal intersect... three sizes of triangles, we end up with about 9 or more cases!