What is the minimum number of different salaries earned by the nine partners of the firm?

michellexnon June 21, 2021

Understanding what is being asked

For this question I interpreted it to mean how many different possible arrangements could there be, so I started going through like this:
1. K I F M G J H L N
2. K L N I F M G J H
3. K L I F M G J H N
etc...
essentially just moving L and N through the sequence since they could go anywhere after K (as long as L was before N). Doing that, I stopped after I realized that there were more than 9 possible combinations. That being said, I realize they're asking for the minimum possible number.
My question is, how did the video arrive at that answer? I don't think I am understanding what is being asked at all. Reading through the discussion posts I see that we can't assume it's a straight sequencing game, but shouldn't that only add to the number of possible combinations? What are we supposed to be figuring out? Can someone help me rephrase the question in a different way so I can understand what is being asked?

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I thought of it like this too. BUT - they are asking the MINIMUM number of salaries. And there are ONLY two that could even have the possibility of having the same as others you count the other two as if they are the same and you come up with the minimum being 7. Its not how many different salaries can you find.. its what is the MINIMUM salaries can you get? Make sense?