Count the Triangles

Can you count the number of triangles in the given figure?

Count the Triangles




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The below is a number puzzle. It should be read left to right, top to bottom.
1
1 1
2 1
1 2 1 1
1 1 1 2 2 1
? ? ? ? ? ?
? ? ? ? ? ? ? ?
Question 1: What are the next two rows of numbers?
Question 2: How was this reached?

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Mr. Buttons was caught in the dilemma of what to ask? And from which owl to ask, since he only had one question. What should Mr. Buttons ask?

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There is a cryptic organization called Cicada 3301 that posts challenging puzzles online, possibly to recruit codebreakers and linguists.