Singapore Primary School Olympiad: Cheryl's Birthday



Alberts and Bernard wanted to know about Cheryl's birthday, so Cheryl gave them two 10 possible dates: May 15, May 16, May 19, June 17, June 18, July 14, July 16, August 14, August 15, August 17. Cheryl only told Alberts the month of her birthday and told Bernard about her birthday. Alberts said: I don't know about Cheryl's birthday, but I know Bernard won't know. Bernard replied: I didn't know Cheryl's birthday at first, but now I know. Alberts also replied: I know that, too. So, what month is Cheryl's birthday?

A very simple question, do not know why the fire up. The solution is also very simple, first list the table, where x is the candidate date:

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

Reasoning one: Alberts said: I do not know Cheryl's birthday, but I know Bernard will not know.

Alberts know the month, he said do not know, it means that the birthday date is not unique, otherwise he will know, and he also said Bernard do not know, that is to say that the month of birth has more than one candidate date. Thus, the month and date are not unique, as can be seen in the figure, May and June have a unique date of May 19 and June 18, so May and June can be excluded, the table is reduced to:

	July	August
14th	X	X
15th		X
16th	X
17th		X

Reasoning two: Bernard answer: I didn't know Cheryl's birthday at first, but now I know.

Bell Sodium knows the date does not know the month, but after shrinking the table he knows the birthday, that is, in table two, the date only corresponds to a unique month, thus the table can be further reduced to:

	July	August
15th		X
16th	X
17th		X

Reasoning three: Alberts said: Then I also know.

Alberts knows the month, does not know the date, he knew, the description form three in the birthday month corresponds is the unique date, then Cheryl's birthday is July 16.

Singapore Primary School Olympiad: Cheryl's Birthday