Wow, that's a lot of replies! Interesting to see the spread of time between the closest and the farthest! I'll hold off on my guess until after 2/15 (I don't want to sway any opinions).
Anywho, a few points of clarification:
If there is more than one person guessing the same date, the first person to guess the date is the "owner" of that date (unless they pick another date).
Sooo.... If you came to the party late, make DARN sure that you haven't picked a date someone else picked.