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mathmath333

  • one year ago

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

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  1. mathmath333
    • one year ago
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    |dw:1440958389425:dw|

  2. mathmath333
    • one year ago
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    \(\large \color{black}{\begin{align} & \normalsize \text{Count the number of triangles in the figure using }\hspace{.33em}\\~\\ & \normalsize \text{ permutation and combination}\hspace{.33em}\\~\\ \end{align}}\)

  3. mathmath333
    • one year ago
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    answer is 28.

  4. mathmate
    • one year ago
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    I also got 28, but splitting it into permutations and combinations would be very messy! Hope someone would enlighten us on this!

  5. Loser66
    • one year ago
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    *

  6. mathmath333
    • one year ago
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    yes counting manually is very easy

  7. mathmath333
    • one year ago
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    i doubt that there is a way P&C way

  8. mathmate
    • one year ago
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    The worry is if there are many panels in both dimensions, then it would be messy if we're not systematic.

  9. ChillOut
    • one year ago
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    I can only split in two cases - I can't fit the smallest triangles in a case where a formula applies. :(

  10. mathmate
    • one year ago
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    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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