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You should be able to derive the person by matching each spilled State/Amount pair back to Sheet 1 and returning the column header where that match occurs. Assuming state + amount uniquely identify the visit, put this in Sheet 2 C11 (it will spill):
=MAP(A11#,B11#,LAMBDA(s,a,
XLOOKUP(
1,
(Sheet1!$A$11:$A$60=s)*
(Sheet1!$B$11:$E$60=a),
Sheet1!$B$5:$E$5
)
))
For each row of the spill, this looks for the row where the state matches s, the column where the amount equals a, and returns the corresponding person name from B5:E5.
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hth
Marcin