BULLET BRAIN BUSTER

He-Man's Birthday

He-Man presents a list of 14 possible dates for his birthday to his friends SpongeBob, Madonna and Screech:

Apr 14, 1999, Feb 19, 2000, Mar 14, 2000, Mar 15, 2000, 

Apr 16, 2000,  Apr 15, 2000, Feb 15, 2001, Mar 15, 2001, 

Apr 14, 2001,    Apr 16, 2001,  May 14, 2001,   May 16, 2001, 

May 17, 2001,   Feb 17, 2002​

heman.jpg

He then announces that he is going to tell SpongeBob the month, Madonna the day, and Screech the year.

 

After he tells them, SpongeBob says  "I don't know Heman's birthday, but neither does Madonna suckers!."

Madonna then says, "That is true, but Screech also does not know He-Man's birthday me hearties!."

Screech says, "Yes and SpongeBob still has not figured out He-man's birthday Mo-Fo's."

Madonna then replies, "Well, now I know his birthday."

At this point, SpongeBob says, "Yes, we all know it now."

 

When is He-man's birthday?

Answer!!!

Answer

 

When SpongeBob claims that Madonna does not know He-Man's birthday, he is saying that he knows that the correct day occurs more than once in the list. In other words, he is saying that He-Man's birthday is not Feb 19, 2000, and the only way he could know that is that he knows that the month is not February. 
So by making this claim, SpongeBob has reduced the list for everyone to:

  • Apr 14, 1999

  • Mar 14, 2000

  • Mar 15, 2000

  • Apr 16, 2000

  • Apr 15, 2000

  • Mar 15, 2001

  • Apr 14, 2001

  • Apr 16, 2001

  • May 14, 2001

  • May 16, 2001

  • May 17, 2001

 

When Madonna says that it is true that he does not know He-Man's birthday, it tells everyone that even with the restricted list the correct day occurs more than once in the list. So everyone can thus eliminate May 17, 2001.

 

Furthermore, the claim that Screech also does not know He-Man's birthday is a claim that Madonna knows that the year occurs more than once on the remaining list.

 

This rules out Apr 14, 1999, and since Madonna could only rule this out by knowing that the day was not 14, everyone can further reduce the list to:

  • Mar 15, 2000

  • Apr 16, 2000

  • Apr 15, 2000

  • Mar 15, 2001

  • Apr 16, 2001

  • May 16, 2001

 

When Screech says that SpongeBob still has not figured out He-Man's birthday, she is telling everyone that given the new list the month occurs more than once and thus rules out May 16, 2001. This tells everyone that Screech knows that the year is not 2001 and the list can be reduced to:

  • Mar 15, 2000

  • Apr 16, 2000

  • Apr 15, 2000 

 

When Madonna then claims to know the date he is saying that the day occurs only once among the 3 remaining choices, thus telling everyone that He-Man's birthday is Apr 16, 2000.