Cheryl's Birthday (aka Birthday problem)

gistfile1.txt

https://en.wikipedia.org/wiki/Cheryl%27s_Birthday

A knows the month
B knows the day

The candidates are:

may        15 16       19
june             17 18
july    14    16
august  14 15    17

A asserts B doesn't know the date. He can only say that with certainty if the month
(that A knows) doesn't contain unique days. That rules out may (which contains 19)
and june (which contains 18).

B, realizing the fact above, reduces the list to:
  
july    14    16
august  14 15    17

and says he knows the date. That implies the the day is NOT 14 (after all, he could not
know the month in that case)

With that in mind, A can reduce the list to:

july          16
august     15    17

And now A says he knows the day. But that means the month can't be august (because it
has two days), hence we rule out august, and the date must be July 16!