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How can I index match unique values?

I asked a question a few hours ago and now I'm trying a different approach on the same issue.

I want to get the largets numbers from a table and the corresponding description.

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The selected cell has the formula =LARGEST(S:S,1) , =LARGEST(S:S,2) and so on...
The issue is that 4 and 5 is the exact same value which makes my INDEX MATCH formula ( =INDEX(P:P,MATCH(U5,S:S,0)) U5 is selected cell) in the cell adjacent to the selected cell find the same product twice.
But if we look in the table to the right which is a copy paste values so that it can be sorted, 4 and 5th largest values are not the same product.

Can I somehow change the index match formula to the n-th of the same value so that it's "correct"?

This is a common problem. You must remove ties so your INDEX(MATCH()) can find all the matches. Consider:

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Note the both Patricia and Mary have the same scores. In C2 enter:

=RANK(A2,$A$2:$A$11,0)+COUNTIF($A$2:$A2,A2)-1

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and copy downwards. Column C tracks column A , but has no ties! (a simple sequential list with no duplicates or gaps)

Finally in E2 and F2 enter:

=INDEX($A$2:$A$11,MATCH(ROWS($1:1),$C$2:$C$11,0))
=INDEX($B$2:$B$11,MATCH(ROWS($1:1),$C$2:$C$11,0))

and copy these downwards.

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