What day of the week was October 10, 1582?

History records that the dates October 1-10 were skipped in the calendar in order to catch the Gregorian calendar back up to the correct date, based off the solstices and equinoxes. Therefore, it didn't fall on any day of the week. The night of September 30 turned into the morning of October 11.

https://en.wikipedia.org/wiki/1582#January%E2%80%93March

The Gregorian calendar was at first only adopted by Roman Catholic countries*, so places like England retained the 'Old Style' Julian calendar in 1582. The 'New Style' Gregorian calendar wasn't adopted by the United Kingdom and its empire until 1752. This sometimes led to switching back and forth between calendars as territories in Canada and elsewhere changed hands between European powers. See https://en.wikipedia.org/wiki/List_of_adoption_dates_of_the_Gregorian_calendar_by_country

So, there was a 10 October 1582 (Old Style) in such non-Catholic places, and it fell on a Wednesday. https://en.wikipedia.org/wiki/1582, https://vbattu.wordpress.com/tag/julian-calendar/

* the shift to the Gregorian calendar in 1582 skipped from 4 October to 15 October for the Roman Catholic church- civil adoption varied, even in Catholic countries- e.g. France made the shift in December that year.

When Pope Gregory XIII introduced the Gregorian calendar in 1582, it was only adopted immediately by a few countries. The Papal States, the Polish-Lithuanian Commonwealth and the German Prince-Bishopric of Passau switched in October 1582, skipping 10 days to realign the calendar.

Meanwhile, Spain and Portugal implemented the reform across their extensive empires, which included territories in the Americas, while other European regions, such as France, Belgium, the Netherlands, Austria, and parts of Switzerland and the Czech lands, adopted it more gradually, sometimes years later, due to local resistance or administrative delays.

https://en.wikipedia.org/wiki/List_of_adoption_dates_of_the_Gregorian_calendar_by_country