Geometric Counting - Triangle Bowtie

Probability Level 1

How many triangles can you find in this figure?

10 38 16 24

Zandra Vinegar by Zandra Vinegar

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5 solutions

Zandra Vinegar Staff
Aug 16, 2015

11 Helpful 0 Interesting 0 Brilliant 0 Confused

Hi, @Zandra Vinegar ! I think you forgot to count these! There are 4 of this type.

Vishnu Bhagyanath - 5 years, 9 months ago

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I was literally just about to comment the same thing, with this image:

Extra Triangles Extra Triangles

Luke Johnson-Davies - 5 years, 9 months ago

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Thank you, 4 beautiful neglected cases!

Zandra Vinegar Staff - 5 years, 9 months ago

I was surprised too on not having 38 as option.

Swapnil Joshi - 5 years, 9 months ago

Yes x4! Thank you. :)

Zandra Vinegar Staff - 5 years, 9 months ago

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I was just marked wrong since I attempted 34 before when there was no option 38.

Vishnu Bhagyanath - 5 years, 9 months ago

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@Vishnu Bhagyanath – Sorry about that -- when I updated the solution, there was no way to correct individual false-negatives. And I used the email informer because this seems like exactly the kind of mistake a problem writer (myself in this case) should own up to fully.

Zandra Vinegar Staff - 5 years, 9 months ago

@Vishnu Bhagyanath – I am looking into fixing this!

Zandra Vinegar Staff - 5 years, 9 months ago
Dhanwinder Singh
Aug 22, 2015

Correct answer is 38

9 Helpful 1 Interesting 0 Brilliant 0 Confused 

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lines = [[1,5,10,16],[15,9,5,2],[3,9,14,18],[17,14,10,4],[1,3,8,15,17],[2,4,11,16,18],[6,7,8,9,10,11,12,13],[1,6],[6,17],[2,13],[13,18],[3,7],[7,15],[4,12],[12,16]]
def check(a):
        global lines
        for i in lines:
                flag = 1
                for j in a:
                        if j not in i:
                                flag = 0
                if flag == 1:
                        return 1
        return 0


counter = 0
for i in range(1,19):
        for j in range(i+1,19):
                for k in range(j+1,19):
                        if check([i,j]) and check([j,k]) and check([k,i]) and not check([i,j,k]):
                                print i, j, k
                                counter+=1
print counter

The result comes out to be 38

Ajay Brahmakshatriya - 5 years, 9 months ago

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An impressive way to have solved it! And thank you for notifying me about the error in this problem.

I've have updated the solution accordingly.

Zandra Vinegar Staff - 5 years, 9 months ago

we know that the correct answer is 38 but we want solution here

Hadia Qadir - 5 years, 9 months ago
Sergio Cristancho
Aug 23, 2015

Actually, there are 38 triangles.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Hadia Qadir
Aug 30, 2015
  1. 4 obvious in the center of each square (8 total) another 8 by combining two of each of the smaller ones (up to 16 now) now to the 4 large obvious ones formed in the larger squares (another 8 so up to 24) then same method of combining for another 8 (up to 32). Now we can deal with the intersection. There's the 2 obvious ones (now up to 34) now for the 4 hidden ones. Take the top point of one large square and the bottom point of the concentric square and you can follow the lines to the intersection to find your hidden triangles there are 4 of these all together adding up to a final total of 38
1 Helpful 0 Interesting 0 Brilliant 0 Confused
Sadasiva Panicker
Aug 23, 2015

16 + 16 + 2 =34

0 Helpful 0 Interesting 0 Brilliant 0 Confused

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