Friday, April 17, 2015

The Logic Puzzle that Stopped the World - Cheryl's Stupid Birthday

Over at LSAC (law school administration council) I imagine there is great rejoicing at the sudden popularity of the "Cheryl's Birthday" logic game. "Great rejoicing" in this case being defined as "a wan individual smiles slightly while polishing his horn rimmed glasses". Yes. He tells himself. I knew it. I knew that the world loved logic games. They just needed some random test from Singapore to show it to them. No matter that we have been producing beautiful logic games for people to become over enthusiastic about since microwave ovens were new technology, but no, let's try not to be bitter about that for now. They have finally come to us. Maybe we can refill our dwindling number of LSAT test takers with logic enthusiasts - oh wait you're only supposed to take it if you want to get into law school...ah well I suppose that could be changed.

The Puzzle - Cheryl's Stupid Birthday

If for some reason you have been living without reddit like a simpleton here is the logic puzzle: It's fun.

Albert and Bernard have just become friends with Cheryl, and they want to know when her birthday is. Cheryl gives them a list of 10 possible dates.

May 15,  May 16, May 19
June 17, June 18
July 14, July 16
August 14, Aug. 15, Aug. 17

Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively. (Yes this sentence is terrible- I copied it precisely)

Albert: I don't know when Cheryl's birthday is but I know that Bernard does not know too.
Bernard: At first I don't know when Cheryl's birthday is but I know now.
Albert: Then I also know when Cheryl's birthday is.

When is Cheryl's birthday?

The Literary and Social Analysis

Additional important observations and the only reason I am writing out this post here - because I could just give you a link to it but I want to provide commentary.

1. I think of Albert, Bernard and Cheryl as elementary school hipsters.

Albert, Bernard and Cheryl- three little punks

 They have old people names bestowed upon them by parents who read many books on sustainable living.  Cheryl is the kind of person who a. refuses tyrannically to tell her friends when their birthday is and then b. pits them against each other.
2. Contrary to what many news sources (including a cartoon from the New Yorker) have asserted it is clear that Cheryl is not the only jerk. Instead of Albert saying, "Hey Cheryl told me that it was ____ (month). If you tell me the day then we can put our information together to fight the vindictiveness of our new friend." instead he says, "I don't know but at least you don't know either! HA HA." Albert and Bernard are also jerks.
3. Math is not logic. This is not a math or maths (thanks brits) problem. Like other sciences, mathematics employs the use of logic to speak about quantity both discrete and continuous. [exeunt classical education]

Hints and the Answer (blah blah)

Recently a facebook friend wrote that her daughter said that something was, "easy peasy lemon squeezy" to which her son replied that actually it was, "difficult difficult lemon difficult"

If you are finding this logic problem "difficult difficult lemon difficult" here are some hints. 

 Hint 1. Just to be clear: Cheryl tells Albert the month that her birthday is in. Cheryl tells Bernard the day that her birthday is on. That sentence is really dumb so I just wanted to clear that up. Mostly what we will do is eliminate possible birthdays based on Albert and Bernard's snotty conversation. 

Hint 2: Albert knows that Bernard does not know when Cheryl's birthday is. Therefore Albert is telling us that Bernard must have been given a date that is repeated. This is how he knows that Bernard does not know. If Bernard was given the date 19th or 18th (both not repeated) he would know immediately what month Cheryl's birthday was in. Albert's bragging that Bernard does not know is effectively telling us that Cheryl's birthday is not in May or June.

Hint 3: Bernard says: Ha! Now I know. Loser pants. 
This tells us that both July 14th and August 14th are out. If Bernard had been given the 14th by Cheryl Albert's elimination of May and June would not have helped him. But since he knows it cannot be these two days

Hint 3: behold! we are left with : July 16 , August 15, and August 17. 
Albert says: I know now too - booger face.
Therefore Albert must have been given the month of July. If he had been given August he still would not know when Cheryl's birthday is because there are two dates left in August. 
The answer is July 16th. 

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