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

Tyler808 on March 19, 2022

Any tips on solving this problem much more fast to save time?

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Emil-Kunkin on March 20, 2022

Hi Tyler,

For minimum/maximum questions, there may have to be some trial and error, but it is best to start by reassessing what the question is referencing. In this case, we are looking at how many must earn different salaries. Since we have one long chain involving seven of the partners (and one shorter chain involving 3, both starting with K) we know that each of the seven in that chain must earn different salaries. The only two who could have the same salary as another partner are the two (L and N) partners in the shorter chain- if they have the same as a partner in the large chain. Since we know there are only two who could have the same salary as another partner, there must be 7 who cannot.