Cheryl's Birthday - Viral Math Logic Puzzle

Описание: "Cheryl's Birthday" is a logic puzzle which gained lots of popularity when published on facebook. That question was posed as part of the Singapore and Asian Schools Math Olympiad for their middle school students to train their math skills. However, it quickly went viral in a few days on the internet.

The question is illustrated below. Albert and Bernard are new friends of Cheryl, and they want to know what her birthday is. To make things interesting, Cheryl gives them a list of 10 possible dates to choose from, which include "May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17". Then Cheryl told Albert the month and told Bernard the date separately about her birthday. After a quick thought, Albert said. I don't know when Cheryl's birthday is, but I am sure that Bernard doesn't know either. Hearing Albert's words, Bernard said. At first I didn't know when Cheryl's birthday was, but I do know now. Then Albert said. Then I also know when Cheryl's birthday is. The question is. Which day is Cheryl's birthday?

The 10 candidate dates given by Cheryl can be illustrated in the following grid. Among these 10 dates, only the 18th and 19th appear once. If Cheryl's birthday is on the 18th or 19th, then Bernard, who knows the date, can guess the final answer. Since Albert is pretty sure that Bernard does not know Cheryl's birthday, it means that the birthday will not be on the 18th or 19th, and then we can get that it will not be in May and June when the 18th or 19th appears. Otherwise, there is a probability that Bernard will know the answer if Cheryl's birthday is on the 18th or 19th. As a result her birthday must be in July or August. According to Bernard, in the remaining 5 dates in July and August, only the 14th appeared twice. If Cheryl told Bernald that her birthday was on the 14th, it is impossible for Bernard to guess her birthday based on the first sentence from Albert. So the 14th will not be the answer. Now, we only have the following three candidate dates left. July 16, August 15 and August 17. Due to the fact that Albert also knows Cheryl 's birthday after Bernald asserts that he already knew the answer, it indicates that the birthday month cannot be in August. This is because August has two possible days, in which Bernald cannot know the exact date. So, the month must be July because there is only one candidate date in July, and the final answer is 16th of July.