Two people are playing a game. The first player announces "January 1". From then on, each player announces a date that's later in the year, subject to the proviso that only the month name or the date of the month can change, not both. The object is to be the one to announce "December 31".
If you're the second player, what date do you announce after the first player has announced "January 1", and what is your strategy from there on?