.The problem can be found at: Logic Problem: When Is Cheryl's Birthday?
Do Not read below this line if you want to solve the problem on your own.
This possible solution has been prepared without looking at other websites.
The Problem States: Albert and Bernard just become friends with Cheryl...
Possible Understanding/Assumption: Albert and Bernard are friends before they met Cheryl.
Possible Understanding/Assumption: Albert and Bernard are friends after they meet Cheryl.
Possible Understanding/Assumption: Albert and Bernard only become friends with Cheryl but not each other.
The Problem States: ...and they want to know when her birthday is.
Possible Understanding/Assumption: Neither Albert nor Bernard know Cheryl's birthday.
I can shorten the problem to: When her birthday is OR Cheryl's birthday is when? OR Cheryl's Birthday = X OR C = X.
The Problem States: Cheryl gives them a list of 10 possible dates.
Possible Understanding/Assumption: One of the 10 dates is Cheryl's birthday.
Possible Understanding/Assumption: None of the 10 dates is Cheryl's birthday because it only says “dates” not birthdates.
Possible Understanding/Assumption: None of the 10 dates is Cheryl's birthday because if any date that is not her birthday can be called a “possible date” then it is possible that all the “possible dates” are not Cheryl's birthday.
The Problem Lists The Dates
The Problem Then States: Cheryl then tells Albert and Bernard separately the month and the day of her birthday respectively.
Possible Question: Why did Cheryl give them a list of possible dates if she was going to tell them anyway?
Possible Answer: I don't yet know, but have suspicions and must proceed for the moment.
Possible Understanding/Assumption: Cheryl told Albert and Bernard in different places at different times.
Possible Understanding/Assumption: Cheryl told Albert the month and Bernard the day. If this was correct, Albert and Bernard would just tell each other what Cheryl told them.
Possible Understanding/Assumption: Cheryl told Albert and Bernard separately at the same time and the same place so that both of them heard what the other was told. It is possible to address two people separately who are in the same room.
Possible Understanding/Assumption: “separately” means she told one the month and the other the date.
Possible Understanding/Assumption: “respectively” means she told one the month and the other the date in that order.
Possible Understanding/Assumption: “respectively” means she told both of them the month and date in that order.
Possible Understanding/Assumption: No matter how she went about it, it resulted in Cheryl telling Albert and Bernard her birthday. It doesn't matter if she told them separately, together, at the same time, in what order, or told each one only part of the birthday. The bottom line is Albert & Bernard now know Cheryl's birthday, each having a part or each having the whole.
Possible Understanding/Assumption: The use of the words “separately” and “respectively” are for confusion. Their placement in the sentence is also for confusion. The compound sentence structure is also used to add to the confusion of confusing words and word placement.
The Problem Then Provides: The conversation of Albert and Bernard.
Possible Understanding/Assumption: The conversation happened in that order and after Cheryl told them the month and the date. How the conversation is formatted on the page encourages this understanding/assumption. However, I am not told by use of the word “then” that the entire conversation happened after Cheryl stopped talking. The word “then” is used elsewhere in the problem to indicate the order of events.
Possible Understanding/Assumption: Albert spoke before Cheryl told them anything. Cheryl then told Albert the month and the date then Cheryl told Bernard the month and the date. Bernard spoke after having heard the same birthday given to both of them. Albert spoke for the second time after having heard the same birthday given to both of them.
Possible Answer To The Question In The Previous Section: The list of possible dates is for distraction and confusion and to lock my thought processes into a set of choices that does not contain the solution. Three clues confirm this. (1) No dates are discussed in the problem by anyone, just a list was given. (2) No clues are given about dates in what Cheryl tells each person, and (3) No clues are given about dates in what Albert and Bernard tell each other.
Possible Understanding/Assumption: What I do know is that Cheryl's Birthday equals what she told Albert and Bernard.
The Possible Solution:The solution has nothing to do with specific dates. The solution is an equation. Furthermore, the solution is a set of equations. As shown in the second section above, if I allow "C" to represent Cheryl's birthday and "X" to represent the unknown birthdate, then:
1. C=X [Cheryl's Birthday is when?]
2. X=A+B [If Cheryl told Albert and Bernard each a different part]
3. C=A+B
4. X=A or B [If Cheryl told Albert and Bernard each the whole birthday]
5. C=A or B
6. X=A confirmed by B and B confirmed by A
7. C=A confirmed by B and B confirmed by A
At some point, I'll check out what the “solution” websites have to say. Please do not comment by posting the solution or information you got from another website. Try it on your own and we shall all learn. In the meantime, we shall also focus on 12 of life's proverbial lessons contained in this problem.
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