When is Denise's Birthday? Ridde with answer.

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 ...

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?
To clarify: neither Albert, Bernard or Cheryl know anything else at the start apart from the fact that Albert has been told the month, Bernard the day (meaning the number of the day), and Cheryl the year.

Total Available Options:

2001: Feb 17, Mar 13, Apr 13, May 15, Jun 17
2002: Mar 16, Apr 15, May 14, Jun 12, Aug 16
2003: Jan 13, Feb 16, Mar 14, Apr 11, Jul 16
2004: Jan 19, Feb 18, May 19, Jul 14, Aug 18

Albert says he doen't know the answer which is obvious as he only knows month and there are atleast two "days" available for a given month.
Then Albert continues by saying that he knows that Berndard doesn't know. This indirectly implies that the correct month doen't have "day" value which appears only once i.e Denise's birthday is not on 11(Apr) or 12(Jun) therefore we can cut out all the dates of April and Jan. Now, available options are:

2001: Feb 17, Mar 13, May 15
2002: Mar 16, May 14, Aug 16
2003: Jan 13, Feb 16, Mar 14, Jul 16
2004: Jan 19, Feb 18, May 19, Jul 14, Aug 18

Then Berdard says he don't know Denise birthday as he only knows the day implying "day" appears more than once in available options so we can remove dates with "day" value that appears only once i.e 17 and 15. Now, available options are:

2001: Mar 13
2002: Mar 16, May 14, Aug 16
2003: Jan 13, Feb 16, Mar 14, Jul 16
2004: Jan 19, Feb 18, May 19, Jul 14, Aug 18

Berdard further says that he is sure that Cheryl don't the exact date inspite of knowing the correct year which indirectly implies that the correct birthday date lies in the year with more than one options which further implies that "13" (Mar) the only available option of 2001 is wrong and all the dates with "13" can be removed from available options. Now, available options are:

2002: Mar 16, May 14, Aug 16
2003: Feb 16, Mar 14, Jul 16
2004: Jan 19, Feb 18, May 19, Jul 14, Aug 18

After that Cheryl says tha she don't know the answer as every year has more than one options available but she is sure that Albert still don't know the answer which implies that all the months available in options of correct year appears atleast twice, further implying the correct year is 2002 or 2003. Now, available options are:

2002: Mar 16, May 14, Aug 16
2003: Feb 16, Mar 14, Jul 16

Albert says,"Now I know her birthday" implying that the correct month appears only once in available options i.e May and the exact birthday date is May 14, 2002.
Bernard says,"I know too."
Cheryl says,"So do I."

Now all of them knows that Denise's birthday without telling each other anything. Cool, right? Let us know in comments if you were able to solve this riddle without seeing the answer.

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