"Forever January" and some Roman history

In my classroom, one of my homeroom students writes the date up on the whiteboard each morning.  Same place, every day.  This past week, my last block of the day was working, and someone remarked, "We've been in January for a long time!"  None of us took notice, because this is middle school and the occasional non-sequitur is de rigueur.  Then we noticed the student looking curiously up at the date.  Gone was January 20th.  It was now mid-day January 80th!  (Middle-school mischief)   Interesting.  So, I prompted the students for a little extra credit.  Seems we had landed in an alternate universe where it is always January. If we are in the perpetual January world, where our February 1st is Januaryland's January 32nd, then what day on our calendar corresponds to January 80, 2016?  

Would love to see your comments with the date you think is the answer, and a clue about how you got there. (Don't use a calendar.  It's more fun.)

So, then I did a little research about January itself and made up the following problem for my other classes the next day.  You can click on Numa P's name to learn more about the 2nd king of Rome below.

 

Numa Pompilius reigned 715–673 BC was the legendary second king of Rome, who reigned from 715-673 BC, succeeding Romulus. Many of Rome's most important religious and political institutions are attributed to him. In fact, King Pompilius gave January and February their names.  January was named after Janus, the god of beginnings and endings.

There is a folktale that King Pompilius liked the name January so much, he decided not to have any other month names.  The whole year would be called January. So, what we think of as February 1^st would have been called January 32.  If the folktale came true and King Pompilius had his way, think about January 80^th, 2016.

a. What month and day would that be on our calendars?

b. What day of the week is it?