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### Best Answer paxwill says

I counted 35 triangles using the hint to label the 2-dimensional sub-shapes. Tussin's suggestion to count vertex triples is also a good idea, but I think better with shapes for some reason. Here are the triangles I found

1-piece: {a, c, d, e, h, i, j , k} = 8 triangles

2-piece: {ad, be, de, eh, fh, fj, gk, hi, ij, jk} = 10 triangles

3-piece: {abc, bce, bfj, cgk, deh, ehi, fgh, ijk} = 8 triangles

4-piece: {abfj, befh, dehi, fgjk, fhij} = 5 triangles

5-piece: {abcde} = 1 triangle

6-piece: {befhij, fghijk} = 2 triangles

7-piece: {abcfgjk} = 1 triangle

Since 8 + 10 + 8 + 5 + 1 + 2 + 1 = 35 that should be the total number unless I missed any.

That's the right answer, good work.

### Janis Leslie Evans says

I counted 19. Let me know if this is wrong. Unfortunately, we can only answer once so I will follow the thread for correct answer if Im wrong.

Well, you got more than half. :) This one's harder to keep track of all the triangles, that's why I hinted at a systematic approach with labels. I'll try to post an easir problem some time.

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### Grace Marguerite Williams says

There are 11 triangles altogether in the abovementioned diagram.

Hey GM, thanks for trying all my shape counting puzzles.

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### I'M BANNED Y'ALL!!!!!!!!!! says

Algorithmic solution: label all the vertices and intersection points and list every subset of three. I count 11 points and (11 C 3) = 165 candidates. Then eliminate the subsets in which one or more pairs of vertices isn't connected by a line.

I'll never ask you what time it is! You may try to teach me how to build a Rolex.

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### brettmw says

The answer is 33. If you look at the diagram and assign letters to each intersection possible triangles are: ABC, ABE, ABF, ABG, ABH, ABI, ACE, ACF, AFG, BCD, BCE, BCF, BCG, BCH, BCI, BCJ, BCK, BDE, BEF, BFK, BGH, BGI, BHI, BJF, BJK, CDI, CDJ, CEH, CEK, CFG, CJI, CKH, and EFK. That's 33.

This is how I would have done it. You get two more with CEF and AEH.

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