The birthday puzzle (DENISE'S REVENGE!)

[latyper]

Having been defeated by round 1 (http://happydiggers.net/showthread.php?1798-The-birthday-puzzle) 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?

[latyper]

I think I got it. I tried to go through it line by line and write down my reasoning as I deleted 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

A=MONTH
B=DAY
C=YEAR
· Albert: I don’t know when Denise’s birthday is, but I know that Bernard does not know.
Albert not knowing when adds nothing. All the months repeat at least once so he wouldn’t know no matter what he was told. If Albert was told June or April Bernard might know because there 11 and 12 only appear once. For Albert to say that he knows Bernard doesn’t know, Albert must not have been told June or April. Therefore all those months can be crossed out.

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

· Bernard: I still don’t know when Denise’s birthday is, but I know that Cheryl still does not know.
Bernard is now looking at the above spread. If Bernard still doesn’t know all the days left that only appear once can be deleted, (17 and 15). For Bernard to know that Cheryl still doesn’t know the answer he must not have been told 13. If he was Cheryl would know it was 13 Mar 2001. Therefore all the 13s can be deleted.

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


· Cheryl: I still don’t know when Denise’s birthday is, but I know that Albert still does not know.
Cheryl not knowing the birthday tells us nothing new. She must have been told 2002, 2003, or 2004. However for Albert to not know any remaining months that only appear once must be in years she wasn’t told. January only appears once, (19 Jan 2004). For Cheryl to know Albert doesn’t know all the 2004 dates must be wrong and can be deleted.

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

· Albert: Now I know when Denise’s birthday is.
Albert only knows the month. For him to know the birthday he must have been told February, May, August, or July. March appears twice and can be deleted.

---------------, ---------------, ---------------, ---------------,
---------------, ---------------, 16 Feb 2003---------------,
---------------, 14 May 2002, ---------------, ---------------,
---------------,, ---------------, ---------------, ---------------,
---------------, 16 Aug 2002, 16 Jul 2003---------------,

· Bernard: Now I know too.
Bernard only knows the day. The only days left are three 16s and a 14. For Bernard to know he must have been told 14. The 16s can be deleted.
---------------,---------------,---------------,---------------,
---------------,---------------,---------------,---------------,
---------------, 14 May 2002, ---------------,---------------,
---------------,---------------,---------------,---------------,
---------------,---------------,---------------,---------------,

· Cheryl: Me too.
Cheryl knows and so do we. 14 May 2002.

[Heptagon_ru]

Thanks! Nice brain rust cleaner :)

[Marius49]

Worst cooperation evar. They could have told each other what they know and the problem is solved. ;p

[Heptagon_ru]

Ah, but it is not said that they are friends (Albert, Bernard and Cheryl). Probably they hate each other and hoped to know the date only by themselves. And that Denise probably wanted to found out who is the smartest one. Alas, they all kinda failed.