## Sunday, April 19, 2015

### Next Level Cheryl Birthday Question

Submitted by iiyamabto on 16 April 2015

Next Level Cheryl Birthday Question
Albert, Bernard and David just became friends with Cheryl, and they want to know when her birthday is.

Cheryl gives them a Iist of 16 possible dates.

May 15    May 16    May 19
Jun 11    Jun 18    Jun 20    Jun 22
Jul 15     Jul 16
Aug 14    Aug 20    Aug 22
Sep 14    Sep 16    Sep 17    Sep 20

Cheryl tells Albert and Bernard separately the month and the day of her birthday, respectively, She then chooses one particular date from the list and tells David, and makes it known to all that the chosen date has a different day and month from her birthday.

Albert: I don't know when Cheryl's birthday is, but l know that Bernard does not know too.

Bernard: I did not know when Cheryl's birthday is, and now I still don't.

Albert: I still don't know when Cheryl's birthday is. Having said that, I am sure David still does not know too.

David: I knew neither the day nor the month right before Albert said his last sentence¹, but after he did, now I know what month it is.

Bernard: I did not know when Cheryl's birthday is right before Albert said his last sentence, but after he did, I know when Cheryl's birthday is.

David: Then I also know when Cheryl's birthday is.

Albert: Now I know too.
So when is Cheryl's birthday?(September 14) What date did Cheryl tell David?(June 20)
1. Last sentence refers to: "Having said that, I am sure David still does not know too."

Solution posted by FinitelyGenerated on 16 April 2015:
1) Albert: I don't know when Cheryl's birthday is, but l know that Bernard does not know too.
Eliminates May, June

2) Bernard: I did not know when Cheryl's birthday is, and now I still don't.
Eliminates 15, 17, 22 (Unique days)

3i) Albert: I still don't know when Cheryl's birthday is.
Eliminates July 16 (Unique Month).
Only the month August and September remains.

3ii) Albert: Having said that, I am sure David still does not know too.
Eliminates August. (Albert knows the month. If David is given September 14 or 20 he would know Cheryl's birthday)
Only the month September remains.

4) David: I knew neither the day nor the month right before Albert said his last sentence¹, but after he did, now I know what month it is.
David was not given August or September as he could not deduce the month at first (step 3i). He was not told August 14 or 20.

5) Bernard: I did not know when Cheryl's birthday is right before Albert said his last sentence, but after he did, I know when Cheryl's birthday is.
Eliminates September 16 - because if it is 16 (unique before Albert said his last sentence), Bernard would have know before step 3ii).

6) David: Then I also know when Cheryl's birthday is.
David was able to eliminate one of 14, 20 so he must have been given June 20 as this is the only 14 or 20 not in August or September (Step 4).
Eliminate September 20.

7) Albert: Now I know too.

Only left September 14 as Cheryl's birthday.

Question submitted by iiyamabto on 16 April 2015
Solution posted by FinitelyGenerated on 16 April 2015

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