# Triangle Brain Teaser

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 responses to “Triangle Brain Teaser”

1. TIN says:

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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2. Faruk says:

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

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3. Faruk says:

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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4. Mr.Chinchie says:

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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• Mr.Chinchie says:

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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5. melvina o’connor says:

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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6. Kim says:

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

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• Kim says:

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

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7. Kim says:

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

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