johnpalmer (![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png)
johnpalmer) wrote2015-04-19 08:33 am
johnpalmer) wrote2015-04-19 08:33 am
"Cheryl's Birthday" puzzle...
I saw there was a viral logic puzzle put out, this girl tells two boys about her birthday - the first gets only the month, and the second gets only the day.
This can be solved but it's a puzzle that bugs me a bit because it's a puzzle based upon that it's a puzzle with a solution. You need to rely on the sufficiency of information to solve it.
That doesn't bother me too much - there are a lot of problems that can be solved by comparing them to another similar problem, recognizing that you can find that they're not just similar, they match - once you figure out how.
For example, a great many puzzles fall into the "pigeonhole principal" - if there are n+1 pigeons and n pigeonholes, at least one hole must have been the entry for more than one pigeon. (And if there are 5n+1 pigeons, one hole must have been the entry for 6 pigeons - or more!)
Anyway: this one's cute, so I figured I'd post a solution behind a cut:
FIrst, there are 10 possible birthdates:
May 15, 16, or 19
June 17 or 18
July 14 or 16
August 14, 15, and 17.
Cheryl decides she wants a threesome on her birthday, but only with competent logicians who communicate to each other. So, she tells two candidates, Albert and Bernard enough information to determine her birthday. First, she gives them this list, and then:
she tells Albert the month of her birthday, and,
she tells Bernard the day of her birthday.
Albert says "Dang it, I don't know her birthday - and I'm sure that Bernard doesn't either!"
Bernard says "Huh. Actually, I know her birthday, now."
Albert replies "Really? Then I do, too!"
What is the birthday?
Well - if Albert had been told May, he doesn't know if Bernard was told the 19th.
If Albert had been told June, he doesn't know if Bernard was told the 18th.
Either of these would have established the month, just by being given the day. Albert (having been told that it was July or August) knows that it's not a month that doesn't share a day with any other month. Wanting to be engaged in this threesome, he alerts Bernard that he's aware of Bernard's lack of knowledge.
Bernard, realizing that Albert knows Bernard doesn't know, can eliminate May and June as well - "if Albert wasn't sure if I knew or not, the month could have been May or June, which has a distinct day. Since he *knew* I didn't know, it had to be a day that shows up more than once."
Once Bernard does that, he can take the day he was given, which shows up in only one month, and determine the birthday.
Since we can eliminate May and June, what are the remaining dates?
July 14 or 16
August 14, 15, and 17.
Now there's a bit of a trick here. If Bernard had been told 14, he still wouldn't know the birthday. But if he was told 15, 16, or 17, he does.
So, there are two options:
1) he says he still doesn't know - Albert does, now, because he was given the month, and knows it has to be the 14th - the only day that repeats. But Cheryl is looking for a threesome - that would have been bad strategizing. Or,
2) he does know - and since Albert was told it was July, he knows it's not the 14th, and therefore must be the 16th.
And thus, on July 16th, Chery, finally has her wishes fulfilled as two boys' hands, in a caressing and loving manner, manipulate her two spare PS4 controllers, while they have a knock-down, drag out gaming session.
(This *may* not have been the original telling - I'm sure I saw one with Xbox 360 controllers instead.)
This can be solved but it's a puzzle that bugs me a bit because it's a puzzle based upon that it's a puzzle with a solution. You need to rely on the sufficiency of information to solve it.
That doesn't bother me too much - there are a lot of problems that can be solved by comparing them to another similar problem, recognizing that you can find that they're not just similar, they match - once you figure out how.
For example, a great many puzzles fall into the "pigeonhole principal" - if there are n+1 pigeons and n pigeonholes, at least one hole must have been the entry for more than one pigeon. (And if there are 5n+1 pigeons, one hole must have been the entry for 6 pigeons - or more!)
Anyway: this one's cute, so I figured I'd post a solution behind a cut:
FIrst, there are 10 possible birthdates:
May 15, 16, or 19
June 17 or 18
July 14 or 16
August 14, 15, and 17.
Cheryl decides she wants a threesome on her birthday, but only with competent logicians who communicate to each other. So, she tells two candidates, Albert and Bernard enough information to determine her birthday. First, she gives them this list, and then:
she tells Albert the month of her birthday, and,
she tells Bernard the day of her birthday.
Albert says "Dang it, I don't know her birthday - and I'm sure that Bernard doesn't either!"
Bernard says "Huh. Actually, I know her birthday, now."
Albert replies "Really? Then I do, too!"
What is the birthday?
Well - if Albert had been told May, he doesn't know if Bernard was told the 19th.
If Albert had been told June, he doesn't know if Bernard was told the 18th.
Either of these would have established the month, just by being given the day. Albert (having been told that it was July or August) knows that it's not a month that doesn't share a day with any other month. Wanting to be engaged in this threesome, he alerts Bernard that he's aware of Bernard's lack of knowledge.
Bernard, realizing that Albert knows Bernard doesn't know, can eliminate May and June as well - "if Albert wasn't sure if I knew or not, the month could have been May or June, which has a distinct day. Since he *knew* I didn't know, it had to be a day that shows up more than once."
Once Bernard does that, he can take the day he was given, which shows up in only one month, and determine the birthday.
Since we can eliminate May and June, what are the remaining dates?
July 14 or 16
August 14, 15, and 17.
Now there's a bit of a trick here. If Bernard had been told 14, he still wouldn't know the birthday. But if he was told 15, 16, or 17, he does.
So, there are two options:
1) he says he still doesn't know - Albert does, now, because he was given the month, and knows it has to be the 14th - the only day that repeats. But Cheryl is looking for a threesome - that would have been bad strategizing. Or,
2) he does know - and since Albert was told it was July, he knows it's not the 14th, and therefore must be the 16th.
And thus, on July 16th, Chery, finally has her wishes fulfilled as two boys' hands, in a caressing and loving manner, manipulate her two spare PS4 controllers, while they have a knock-down, drag out gaming session.
(This *may* not have been the original telling - I'm sure I saw one with Xbox 360 controllers instead.)