Brenda's Birthday
Albert and Alex are Brenda's good friends. They just found out that her favorite color is red and thought a bouquet of red roses would be a great birthday present for her. However, the problem is that they do not know her birthday. Brenda gives them 14 possible dates:
July 12, July 17
August 8, August 9, August 10, August 19
September 8, September 16, September 17
October 10 , October 16, October 22
November 17, November 19
Brenda then tells Albert the month and Alex the date, separately.
Albert - ''I do not know Brenda's birthday but I can say for sure that Alex does not know too.''
Alex - ''Before you said that I did not know but now I know already.''
Albert - ''Then now I also know.''
When is Brenda's birthday? Your answer should be the product of the month and date.
The answer is 209.
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1 solution
First let's deduce the month Brenda told Albert. Since Albert is 100% sure that Alex does not know, the month revealed to Albert MUST have ALL its possible dates duplicated - meaning the same dates appear in at least one other month. Here we eliminate July, August and October. July has 12th, August has 9th while October has 22nd which do not appear in any other month so if Albert was told any of these months, he cannot say FOR SURE that Alex does not know. After hearing what Albert said about being sure that Alex does not know, Alex would have figured that Brenda told Albert either September or November. Since Alex knows Brenda's birthday by then, he cannot possibly be told 17th as the date as 17th appears in both September and November so he would still be unsure. The fact that he is sure, Brenda's birthday cannot be in September as there are still two other possible dates since September has three possible dates. However, November only has two so if Alex was not told 17th, he must have been told 19th.
19x11=209...!!!!!