cwilper/gist:ec9c4f8925f1d181dfdc

## gistfile1.txt
See http://www.washingtonpost.com/news/morning-mix/wp/2015/04/14/when-is-cheryls-birthday-the-math-problem-that-stumped-the-internet/

Cheryl's Birthday Reasoning
===========================

Cheryl tells Albert the month of her birthday, and she tells Bernard
the day of her birthday. She also tells them both that her birthday
is one of the following 10 dates:

May        15 16        19
June             17 18
July    14    16
August  14 15    17

Given: Albert knows the month, which is May, June, July, or August.
Given: Bernard knows the day, which is 14, 15, 16, 17, 18, or 19.

First, Albert states that he doesn't know her birthday. This in
itself doesn't convey any new information, as all months have
more than one possible day.

But when Albert states that he knows that Bernard doesn't know her
birthday, he is revealing some new information. The only way Bernard
could not know the month is if the day is not enough information to
deduce the month. Looking at the possible days, which of them is
a candidate in only one of the possible months? Answer: 18 and 19.
These days occur in May and June. So Albert has just indirectly
revealed that the month is either July or August.

Bernard now knows that the month is either July or August. When
he says he now knows her birthday, he is also revealing some new
information. Bernard could only know her birthday month if the
day (which he knows) only occurs in one of the candidates. This
means the day is definitely not the 14th, as that day is a candidate
in both July and August. So Bernard has just indirectly revealed
that the date is either July 16th, August 15th, or August 17th.

Later, when Albert says he knows when her birthday is, he is
revealing some new information to us. The only way he could
know when her birthday is among the three candidate dates is
if the month (which he knows) is sufficient to identify the date.
August has two candidate dates, so that is excluded. So Albert has
just revealed to us that the date is July 16th.
	See http://www.washingtonpost.com/news/morning-mix/wp/2015/04/14/when-is-cheryls-birthday-the-math-problem-that-stumped-the-internet/

	Cheryl's Birthday Reasoning
	===========================

	Cheryl tells Albert the month of her birthday, and she tells Bernard
	the day of her birthday. She also tells them both that her birthday
	is one of the following 10 dates:

	May 15 16 19
	June 17 18
	July 14 16
	August 14 15 17

	Given: Albert knows the month, which is May, June, July, or August.
	Given: Bernard knows the day, which is 14, 15, 16, 17, 18, or 19.

	First, Albert states that he doesn't know her birthday. This in
	itself doesn't convey any new information, as all months have
	more than one possible day.

	But when Albert states that he knows that Bernard doesn't know her
	birthday, he is revealing some new information. The only way Bernard
	could not know the month is if the day is not enough information to
	deduce the month. Looking at the possible days, which of them is
	a candidate in only one of the possible months? Answer: 18 and 19.
	These days occur in May and June. So Albert has just indirectly
	revealed that the month is either July or August.

	Bernard now knows that the month is either July or August. When
	he says he now knows her birthday, he is also revealing some new
	information. Bernard could only know her birthday month if the
	day (which he knows) only occurs in one of the candidates. This
	means the day is definitely not the 14th, as that day is a candidate
	in both July and August. So Bernard has just indirectly revealed
	that the date is either July 16th, August 15th, or August 17th.

	Later, when Albert says he knows when her birthday is, he is
	revealing some new information to us. The only way he could
	know when her birthday is among the three candidate dates is
	if the month (which he knows) is sufficient to identify the date.
	August has two candidate dates, so that is excluded. So Albert has
	just revealed to us that the date is July 16th.