**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!

## 16 replies on “Triangle Brain Teaser”

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

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? Could you be more specific? Maybe an image, or describe it using some of the numbers of the triangles from my images?

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

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Good eye!

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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

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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 🙂

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

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I’m not seeing it- can you send a link to an image explaining it?

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I am sorry i meant between triangles 13, 24, 25, 26, 27, 28.

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Ah! Nice one! I’ll update the post. Thanks for pointing it out!

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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

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Good luck! Let me know if you find the elusive #41!

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[…] 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/ […]

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

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Iv got 42, then 43 and no 40 haha not 41

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Finally got 41!!! I overcounted two triangles upside down to get my 43

Have been wrecking everyones head with this

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