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This question already has an answer here:

Years ago, there was a small kingdom, in which there was a king. His daughter was so beautiful, that people around the world went there to marry her. But the king would allow the most clever man to be married with his daughter. So, he set a riddle and told it to every possible groom. The riddle was the following:

1 1

2 1  

1 2 1 1

...

The task of them was to feel the fifth row with the dots. Does anybody know the answer to this riddle? Good luck!

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marked as duplicate by Deusovi, Engineer Toast, f'', Gamow, Zandar May 17 '16 at 18:19

This question has been asked before and already has an answer. If those answers do not fully address your question, please ask a new question.

1
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1 1 1 2 2 1 (previous line - One One, One Two, Two Ones.)

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1
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The pattern is that:

Each row describes the numbers in the previous row.

So, to more fully describe each row:

1 - Start of pattern
1 1 - The previous row had one 1
2 1 - The previous row had two 1s
1 2 1 1 - The previous row had one 2 and one 1

In fact, this pattern is an exact match for A005150 in the OEIS. That continues the pattern for much longer and shows details you can't see in the relatively short excerpt in this question.

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