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Define a summary field as the "count of" your date field. (Or any other field that is never empty)
Sort your records by date to group them by same date.
In a summary report, you can put this summary field inside a sub summary layout part "when sorted by" your date field.
The summary field will then show the number of records for each date. If you remove the body layout part from this layout, put the date field inside the sub summary part and sort your records by date, you'll see each date listed once with the record count for each.