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# hard counting

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145
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How many distinct triangles can be drawn using three of the dots below as vertices?

Jul 13, 2020

#1
+28021
+1

I count 14 ....  anyone else?   (edited)

Jul 13, 2020
edited by ElectricPavlov  Jul 13, 2020
#3
+732
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i got 18... i'm  not sure if im right though

#2
+732
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hmm I think a better approach to this problem is to use complementary counting.

There are $$\dbinom{6}{3}=20$$ ways to choose 3 points to make a triangle. However  of these ways are just straight lines, so $$20-12=\boxed{18} \text{ triangles. }$$

I'm not sure if this is right, so please let me know if it's correct or not!

:)

Jul 13, 2020
#4
+111626
+1

Hi Loki,

Your logic sounds good to me.

you have a typo though

Melody  Jul 13, 2020