A Math Problem from Singapore Goes Viral(nytimes.com)

  import collections

  dates = '''may 15 may 16 may 19
             jun 17 jun 18
             jul 14 jul 16
             aug 14 aug 15 aug 17 '''

  def dups(xs,pos):
      return [k for k,v in collections.Counter(x[pos] for x in xs).items() if v>1]

  days = dates.split()[1::2]
  months = dates.split()[0::2]
  dts = [(d,m) for d,m in zip(days, months)]
  # A doesn't know, and knows B doesn't know-- cut days occurring once
  dts = [dt for dt in dts if all(not(dt[0]==d or dt[1]==m)
           for d,m in zip(days, months) if days.count(d)==1)]
  # now B knows-- cut dup days
  dts = [dt for dt in dts if dt[0] not in dups(dts,0)]
  # A also knows-- cut months with more than 1 day
  dts = [dt for dt in dts if dt[1] not in dups(dts,1)]
  print dts

  Date: 01/21/2006 at 00:43:08
  From: Eddie
  Subject: P -> Q <> ~Q -> ~P

  A teacher told the month of her birthday (let's call it M) to Peter,
  and the day of her birthday (let's call it D) to John.
  Then, the teacher showed a set of dates, and asked Peter
  and John which one was her birthday:

  4 Mar, 5 Mar, 8 Mar 
  4 Jun, 7 Jun 
  1 Sep, 5 Sep
  1 Dec, 2 Dec, 8 Dec 

  Peter said, "If I don't know the answer, John doesn't know, too."
  John said, "At first I really didn't know, but now I know."
  Peter said, "I know, too."

  What is the teacher's birthday?

  *“Can you figure it out now?” she asked Bernard.

  Albert: No, he doesn't.

  Bernard: Now I do.

  Albert: Now I do, too.