Triangle Brain Teaser

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UPDATE on 10/31/2012– My answer is wrong. Eagle-eye commenters found two more triangles to add to my answer, which are pointed out in the comments, and below the gallery in the UPDATE sections.

I came across a brain teaser on Facebook that a friend had commented on, and I’m pretty much going to get obsessed with any brain teaser, so I had to give it a shot (or 3).

It went like this.

How Many Triangles are in the Picture Below?

I counted it at first and was sure I missed some, so I went back and tried it again and found a few more. Then, on my third try, I found what I believe is all of them. I checked a few more times and it’s all I can find.

Then, the poster of the facebook question displayed the answer to everyone as one less than what I had come up with. So, it bothered me enough that I decided to completely waste my time putting this together. The gallery shows how I found my answer.

UPDATE on 10/10/2012– Faruk pointed out in the comments I missed one more triangle. You combine 19+20+21+26.

UPDATE on 10/31/2012– Mr.Chinchie found another one! You combine 13+24+25+26+27+28. So the current answer is now 41 triangles. If anyone finds another, let me know!

Comments

16 responses to “Triangle Brain Teaser”

October 2, 2012

TIN

41. you still forget to count the inner inner triangle.

Reply
1. October 2, 2012
  
  admin
  
  ? Could you be more specific? Maybe an image, or describe it using some of the numbers of the triangles from my images?
  
  Reply
October 10, 2012

Faruk

The 40th triangle is composed off the triangles numbered 19+20+21+26

Reply
1. October 10, 2012
  
  admin
  
  Good eye!
  
  Reply
October 10, 2012

Faruk

40 triangles. Lets put the vertices tags. Starting from the upper vertex and moving down and along a line from the left to right the vertices on the lines are:

1
2 3
4 5 6 7 8
9 10 11 12
13 14 15 16 17
18 19 20 21 22

Now the triangles are made off the vertices like:

All triangles having area equal to uppermost triangle
1. 1-2-3
2. 2-4-6
3. 2-3-6
4. 3-6-8

5. 4-13-14
6. 4-6-14
7. 6-14-16
8. 6-16-8
9. 8-16-17

10. 13-18-19
11. 13-14-19
12. 14-19-20
13. 14-16-20
14. 16-20-21
15. 16-17-21
16. 17-21-22

17. 5-7-15 -inverted

All triangles of the smallest area:

18. 4-5-9
19. 5-9-10
20. 5-10-6
21. 6-10-11
22. 6-11-7
23. 7-11-12
24. 7-8-12

25. 9-10-14
26. 10-14-15
27. 10-15-11
28. 11-15-16
29. 11-16-12

All triangles having area equal to four times the area of the top most triangle

30. 1-4-8
31. 2-13-16
32. 3-14-17
33. 4-18-20
34. 6-19-21
35. 8-20-22

36. 4-8-20 -inverted

All triangles having area bigger than all the above ones

37. 1-13-17
38. 2-18-21
39. 3-19-22

And the biggest one

40. 1-18-22

Reply
1. October 10, 2012
  
  admin
  
  I can’t quite picture which vertices you’re labeling with each number. Any chance you could post a link to an image with the vertices labeled?
  
  I’m glad I’m not the only one who got overly interested in trying to explain how to solve this puzzle 🙂
  
  Reply
October 18, 2012

Mr.Chinchie

There is another one between 33, 24, 25, 26, 27, and 28, so there should be 41

Reply
1. October 29, 2012
  
  admin
  
  I’m not seeing it- can you send a link to an image explaining it?
  
  Reply
  1. October 31, 2012
    
    Mr.Chinchie
    
    I am sorry i meant between triangles 13, 24, 25, 26, 27, 28.
  2. October 31, 2012
    
    admin
    
    Ah! Nice one! I’ll update the post. Thanks for pointing it out!
October 29, 2012

melvina o’connor

I’ve been stuck on it since this morning thanks to Pepper Club..they gt 41 and I gt 45…so I’m gonna recount till I get 41…is this the preferred answer

Reply
1. October 29, 2012
  
  admin
  
  Good luck! Let me know if you find the elusive #41!
  
  Reply
January 3, 2013

Brain Teaser | How many triangles do you see

[…] Comment your answer below and if you would like to see the ‘answer’ you can check out this website http://jeremyjon.es/uncategorized/triangle-brain-teaser/ […]

Reply
April 29, 2015

Kim

I got 43! Ive done it a few times now. I wish I could post a pictue of it!

Reply
1. April 29, 2015
  
  Kim
  
  Iv got 42, then 43 and no 40 haha not 41
  
  Reply
April 29, 2015

Kim

Finally got 41!!! I overcounted two triangles upside down to get my 43
Have been wrecking everyones head with this

Reply