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Default Detect strings in a range

I have a duty rota consisting of a range of cells containing names. The first
column of the range contains dates. The column headings are the duties.
I want to present this information in a different way for the benefit of
those on duty. I want to construct a new table, ideally on a different
worksheet, containing a list of names down column 1, the duties across the
column headings in row 1, and dates in the rows. I want the people to be able
to look at this table to find out quickly which dates they are responsible
for.
I began by trying to use VLOOKUP until I foiund that this requires an
alphabetically-sorted table.
I can explain the function like this:
I want to match a string within a range of cells.
If true, I want to print the contents of the row in the date column.
If false, I want a blank cell.
 
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