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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!

By Jerry Jones

JavaScript Engineer for Automattic, living simply in rural MO.

16 replies on “Triangle Brain Teaser”

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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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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