"Fun" Math problems thread! (Yay)

General
63

That makes sense, and is a way less complicated way to define a triangle.

64

Iā€™m at 25ā€¦

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65

Uh, interesting, youā€™ve got more than I did ^^

66

Iā€™m double checking to make sure I didnā€™t double count.

67

I hope so! Thatā€™s the definition of a triangle :wink:

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68

No wait, no, I failed in counting my stuff on my paper, I have 24, not 25.

Whatā€™s the answer?

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69

24 is what I got, give me a minute to write how I got to the number ^^

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70

YAY.

Now Iā€™m going to get some food.

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71

First, letā€™s use our handy, dandy crayons:

I used the intersection points as a ā€¦ starting pointsā€¦ and colored each line that got through that starting point red, and ever line that could be used to complete a triangle green. After those three drawings, there was no intersection left, that wasnā€™t already completely covered by the three previous.

In the first one, I can freely choose 2 out of 4 for each of the 3 green lines, whereas in the other two, I can always choose 1 out of 3 green lines to complete the red, which leads to the following:

Of course, I couldā€™ve also written just 3 instead using the fancy binomial coefficient thingy (and I did so in the first half), but I just felt like writing one more coefficient, in a hope that it helps understanding my word blurbs.

72

I also find 25

73

Can you tell me, which one I am missing?

74

Oops, I meant 24, sorryā€¦
(I hadnā€™t read your answer, but I used the same technique, except I counted them by hand instead of taking a pen and paper)

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