mathmath333
  • mathmath333
Count the number of triangles in the figure using permutation and combination
Mathematics
jamiebookeater
  • jamiebookeater
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mathmath333
  • mathmath333
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mathmath333
  • mathmath333
\(\large \color{black}{\begin{align} & \normalsize \text{Count the number of triangles in the figure using }\hspace{.33em}\\~\\ & \normalsize \text{ permutation and combination}\hspace{.33em}\\~\\ \end{align}}\)
mathmath333
  • mathmath333
answer is 28.

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mathmate
  • mathmate
I also got 28, but splitting it into permutations and combinations would be very messy! Hope someone would enlighten us on this!
Loser66
  • Loser66
*
mathmath333
  • mathmath333
yes counting manually is very easy
mathmath333
  • mathmath333
i doubt that there is a way P&C way
mathmate
  • mathmate
The worry is if there are many panels in both dimensions, then it would be messy if we're not systematic.
ChillOut
  • ChillOut
I can only split in two cases - I can't fit the smallest triangles in a case where a formula applies. :(
mathmate
  • mathmate
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!

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