Having been defeated by round 1 I saw a chance to reclaim my honor with The Birthday Puzzle (DENISE'S REVENGE). I haven't read the answer on this one and will post again if I work it out. Don't forget to use spoiler tags if you get it.

Albert, Bernard and Cheryl became friends with Denise, and they wanted to know when her birthday is. Denise gave them a list of 20 possible dates.
17 Feb 2001, 16 Mar 2002, 13 Jan 2003, 19 Jan 2004
13 Mar 2001, 15 Apr 2002, 16 Feb 2003, 18 Feb 2004
13 Apr 2001, 14 May 2002, 14 Mar 2003, 19 May 2004
15 May 2001, 12 Jun 2002, 11 Apr 2003, 14 Jul 2004
17 Jun 2001, 16 Aug 2002, 16 Jul 2003, 18 Aug 2004
Denise then told Albert, Bernard and Cheryl separately the month, the day and the year of her birthday respectively.
The following conversation ensues:

  • Albert: I don’t know when Denise’s birthday is, but I know that Bernard does not know.
  • Bernard: I still don’t know when Denise’s birthday is, but I know that Cheryl still does not know.
  • Cheryl: I still don’t know when Denise’s birthday is, but I know that Albert still does not know.
  • Albert: Now I know when Denise’s birthday is.
  • Bernard: Now I know too.
  • Cheryl: Me too.

So, when is Denise’s birthday?