Can you solve mathematics in Singapore where the mathematics level is the highest regular in the world?

Every four years Singapore is targeting elementary and junior high school students all over the world "International mathematics and science education survey"It is known to always be ranked in the top class, mathematical problems for students who have been asked in such Singapore are topics in the world.

Can you solve the maths question for Singapore schoolkids that went viral? | Science | The Guardian
http://www.theguardian.com/science/alexs-adventures-in-numberland/2015/apr/13/can-you-solve-the-singapore-primary-maths-question-that-went-viral

"P5" logic question is actually a Math Olympiad question for Sec 3 and 4 students | Mothership.SG
http://mothership.sg/2015/04/p5-logic-question-is-actually-a-math-olympiad-question-for-sec-3-and-4-students/

What triggered a topic worked for a TV station in SingaporeKenneth Kong's FacebookA picture posted with a comment "P5 (for fifth grade fifth grade students)". Even adults are getting lost as to answers.


【problem】
Albert and Bernard have become friends with Cheryl. Albert and Bernard wanted to know Cheryl 's birthday, but Cheryl taught us only the following 10 dates, one of which is the actual birthday.

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

Cheryl also taught Albert only the birthday moon, and Bernard taught only the date of her birthday. After that, Albert and Bernard are talking in the following flow.

Albert: I do not know Cheryl 's birthday and Bernard does not know Cheryl' s birthday.
Bernard: I did not know Cheryl 's birthday at first, but now I understand.
Albert: I knew Bernard as well as I knew.

Based on these conditions, it is a problem that leads Cheryl 's birthday, but will it be possible to reach a correct answer without fail?

【answer】
* Since we are posting an example answer of the problem from the following, please be careful if you want to solve the problem by yourself.(We will call Albert "A", Bernard "B", Sheryl "C" below)

First, because C's birthday candidate spans several months, A who knows only the month of birth can not identify C's birthday.

In order to organize information, we will group birthday candidates on the date.
· 14th group
July 14
August 14
· 15th group
May 15
August 15
· Group of 16th
May 16
July 16
· Group on 17th
June 17
August 17
· Group on 18th
June 18
· Group of 19th
May 19

Looking at the organized information, only the 18th and 19th groups have only one birthday candidate. For example, if 18th or 19th is C's birthday, 18th is June, 19th is only in May, so B can identify C's birthday. If A was told from C that the month of birthday is June or May, the first remark should be "B might know C's birthday". However, in fact, "B also does not know the birthday of C" is said. That means that C's birthday candidate heard by A will be July / August, not May / June.

The birthday candidates extracted May / June are as follows. Next, B who heard the remark of A identifies C's birthday. The fact that B who knows only the date of birth could identify the birthday can exclude the 14th group which can not be decided as July or August as the birthday from the birthday candidate.
· 14th group
July 14
August 14
· 15th group
August 15
· Group of 16th
July 16
· Group on 17th
August 17

Excluding the 14th group from the birthday candidate will be as follows.
· 15th group
August 15
· Group of 16th
July 16
· Group on 17th
August 17

Finally, since A who was able to hear B's remarks could identify C's birthday, in July's July 's month with only one birthday candidate' s dateJuly 16It is understood that it is C's birthday. I can not identify my birthday because I have two birthday candidate dates in August.

By the way, this problem is in SingaporeSASMOI understand that it is a problem for junior high school second grader to junior high school third grader that was qualified at the mathematics Olympic Games which is operated by the student.