Do this maths. It R Hard.
-
Or, just use a sat solver, once you know some algorithms to look for.
Or do it on paper.
-
You are making the jokes so very difficult.
-
I don't see what's so funny about 2-sat.
-
Or, just use a sat solver, once you know some algorithms to look for.
Everybody keeps talking about SAT solvers. But by the time one was programmed for this problem, probably Cheryl would be married with children.
-
But by the time one was programmed for this problem,
I don't feel that this problem was difficult enough to be worth using the sat solver; it's pretty easy to tell that the correct answer was correct once it was found. The only issue with getting/verifying the correct answer was in translating the way the statements were written, which would have been an issue when trying to enter it into the sat solver too, so it wouldn't have helped.
-
With this type of problem, in an interview situation, they're not really looking for the right answer anyway; they're far more interested in how you work it out
-
I don't feel that this problem was difficult enough to be worth using the sat solver;
It was supposed to be a joke. I was starting with the assumption that the reason Cheryl gave this problem to Albert and Bernard is because they are both chasing her and she wants to know which one is smarter (or maybe get rid of them, but where's the fun in that?). That being the case, it is up to the observer to "win" by proving out as the smartest of the group...gets the answer without being told month or day.
But if the observer is going to spend time programming a SAT...lose...
But since I had to explain it, well, fail!
-
Why bother finding an answer for a puzzle once you've solved it?
-
I let Dischorse trick you into thinking my response was directed AT you, but rather it was directed @Captain in agreement with you. -quoting you made it be "in reply to" you, where it should have been in reply to Captain with a quote from you.
So my fault for failing to dischorse properly... mea culpa?
And also, I found your joke to be funny enough (though not quite like-worth!)
-
"I don't know when Cheryl's birthday is, but I know that Bernard does not know too."
"At first I don't know when Cheryl's birthday is, but I know now."
"Then I also know when Cheryl's birthday is."
-
If Albert knows for sure that Bernard can't know the date, then the month Albert's been given must be one where all the possible days recur in other months (for example, if Albert had been told May, that would leave open the possibility that Bernard had been told 19, which only occurs in May, and therefore reveals the whole birthday).The only such month is August. So Albert's been told August, and his first statement is equivalent to announcing this.
Having told Albert August, Cheryl must then have told Bernard 14, 15 or 17. Combining any of these with August, which Bernard can deduce from Albert's statement, is enough for Bernard to identify the birthday and make his statement true.
Therefore, Albert is mistaken when he claims to know the birthday on the strength of Bernard's announcement.
-
Dang. Missed that July also shares all its days with another month. Recalculating...
If Albert knows for sure that Bernard can't know the date, then the month Albert's been given must be one where all the possible days recur in other months (for example, if Albert had been told May, that would leave open the possibility that Bernard had been told 19, which only occurs in May, and therefore reveals the whole birthday).The only such months are July and August. So Albert's been told July or August, and his first statement is equivalent to announcing this.
If Cheryl told Albert July, she must also have told Bernard 14 or 16. 14 would not have let him use Albert's announcement to distinguish July 14 from August 14, so she didn't do that. July 16 is therefore possible.
If Cheryl told Albert August, she must also have told Bernard 14, 15 or 17. 14 would not have let him use Albert's announcement to distinguish July 14 from August 14, so she didn't do that. 15 and 17 are both still possible, but Albert would have no way to distinguish them on the strength of Bernard's announcement. So Cheryl can't have told him August, and the birthday is July 16.
-
I got the correct answer right away, but I cba to rtf and see if a concise explanation has been posted yet. Since @flabdablet is still stumbling over it in the last post, I'll assume that no.
[spoiler]July 16[/spoiler]
- Albert doesn't know the date; knowing only the month, he couldn't anyway.
- Albert knows that Bernard doesn't know
- Therefore he knows that Bernard cannot know
- Thus Bernard cannot know a number that uniquely identifies the month
- By revealing this fact, he has told Albert that the month isn't May or June
- By ruling out May and June, Albert disambiguated Bernard's number
- Thus the number isn't 14, or Albert still wouldn't know
- By revealing that he now knows the date, Albert tells us that it must be July
- Otherwise, ruling out the 14th would have left either Aug 15 or 17 for him.
More importantly, has anybody pointed out the gramming in Bernard's statement yet, or @Algorythmics' ‘fair’ fail?
-
It's been mentioned, the question is from singapore
-
That would be 17 June...
[spoiler] Since getting rid of all the unique days leaves you with just one month with just one day left[/spoiler]
-
that's the most wrong I've seen so far. How does that work?
-
It doesn't seem that hard to me, but maybe my logic is wrong (Could very well be I looked at it like 20 secs).
[spoiler]
First the guy who knows the days states that he does not know which date it is.
So it isn't a unique day So May 19, June 18th and August the 15th are off.
Then he states that the they guy knowing the month also doesn't know this.
The Guy who knows the months then states that he now does know it.
That shows that his month now only has one day left which would be June.
Having stated that he now does know the guy knowing the months also knows.
[/spoiler]
-
Without reading anyone else's posts:
[spoiler]
A knows the month
B knows the day
A knows that B does not know
=> all days in the month are in at least one other month
=> month is July or August
B now knows
=> exactly one of July and August includes that day
=> day is 15, 16, or 17
A now knows
=> month includes exactly one of 15, 16, and 17
=> month is July
=> day is 16
C's birthday is on 16 July []
[/spoiler]Difficulty rating: short stroll in the park on a pleasant day. The rate-limiting factor was extracting the data from the list at each step, not deducing the method.
-
[spoiler]First the guy who knows the days states that he does not know which date it is.[/spoiler]
First guy knows the month.
-
Ah there goes the planet...
Then I would go for July the 16th
-
I am a necromancer.
Here is another problem appearing in the news if you are interested:
This is from a UK GCSE maths paper, which puts the students at 16. It's far easier than the other one IMO although comparison is difficult since they are different processes, and while I was taught this process, I was not taught the one featured in the original problem of this thread.
The correct answer is featured in the question, and the test is to successfully arrive at it. My answer will be posted subsequently.
If anyone has trust issues, my answer has a hash of: E2F09834045D4DB6ECC20EE203A493BFB598955F
as calculated by http://www.hashemall.com/
note this hash is against the raw of the answer which will be inside spoiler tags but will not include the spoiler tags themselves.inb4 derailing of thread to discuss hashing.
-
[spoiler]N must be 10 or -9 by the quadratic formula, -9 is nonsenical so n must be 10[/spoiler]
so i know the answer, but i don't know how it relates to the problem.... i mean it is just simple algebra based on the formula given. what do the words have to do with anyhting‽
-
you have to show how you translate the words into the answer given.
-
If there are 10 sweets, then the probability of picking two orange sweets in a row is 6-in-10 then 5-in-9; multiply to 30-in-90, then simplify to 1-in-3.
QED.
-
you have to show how you translate the words into the answer given.
when why is there a formula for the solution to N as part a‽seriously, if you want me to solve the word problem don't just give me the solution at the end, because i'll always solve the formula and get the correct answer in less time than it takes to work out the word problem.
just ask me to solve for n and be done with it!
</rant>
-
If there are 10 sweets, then the probability of picking two orange sweets in a row is 6-in-10 then 5-in-9; multiply to 30-in-90, then simplify to 1-in-3.
yes, that is how to work it out. which i figured out while writing my rant.
but my
stands, why give me the correct answer then tell me to show my work on how i got from the problem to the answer‽
-
This is how UK exam papers work, they have questions asking you to find the simplest form of the formula to solve, and then questions asking you to solve the formula, so you can get marks for each part independently
-
[spoiler]
probability p1 is 6 / n
probability p2 is p1 * (5 / (n-1)
p1p2 = (6 / n) * (5 / (n - 1))
p1p2 = 1 / 3
1 / 3 = (6 / n) * 5 / (n - 1))
1/3 = 30 / n * (n - 1)
1/3 = 30 / n^2 - n
1 = 90 / N^2 - n
N^2 - n = 90
N^2 - n - 90 = 0
[/spoiler]
-
This is how UK exam papers work, they have questions asking you to find the simplest form of the formula to solve, and then questions asking you to solve the formula, so you can get marks for each part independently
... okay i get that, but it still alloys me that you gave me a word problem followed by "here's the answer to the word problem! now tell me how you got from the word problem to the answer!" when my answer is always going to be "i read the next question and it told me the correct answer to this one"
-
but they aren't asking you how you know the answer, they are asking you to show the answer is true
-
Exactly; they're giving a list of facts, and asking for proof it's self-consistent and non-contradictory
-
which forces me to solve the problem in the exact route they want it solved.
it was often proved in my college maths that i think very differently than my classmates, often my thinking takes massive, yet mathematically justified, shortcuts, occasionally it takes the scenic route. for every exam after first year i basically had reserved office time with the maths professor so we could go over my paper and verify that my logic was sound because i never followed the path the professor had made the answer key for.
i always started in the same place, and i (baring accidentally swapping a + for a - when doing the sums at the end, which happened occasionally) always got to the same answer in the end.
-
[spoiler]1/3 = P(both orange)
= P(first sweet orange) * P(second sweet orange|first sweet orange)
= 6/n * 5/(n-1)
= 30/n(n-1)
=>n(n-1)= 3*30 = 90
=> n^2 - n -90 = 0
[][/spoiler]
-
which forces me to solve the problem in the exact route they want it solved.
For a standardized test you almost have to do that though. You can't allow differences between graders to affect test scores. There has to be only one right answer, and when the answer is a proof, it therefore has to be constrained tightly to ensure there's only one valid proof.
-
Which is the big drawback with standardised tests: they encourage homogenous thinking, not allowing for creativity
-
i have a deep seated and i think completely justified dislike for standardized testing because:
they encourage homogenous thinking, not allowing for creativity
QFFT
now i'm not advocating accepting 1+1=3 as correct, but if i don't add the way common core wants me to add, but i do get the same correct answer every time then I should get full marks because i got the correct answer and my proof of the answer, while not necessarily optimal is also correct.
-
if i don't add the way common core wants me to add
Then you didn't learn what the teacher was trying to teach.
If I'm teaching my brother how to make a two-column site, and he installs Wordpress and finds a two-column theme, he's clever, but he hasn't shown me that he learned what I tried to teach him, has he?
Most standardized tests aren't very good, but I can see the merit in testing students on methodology.
-
Then you didn't learn what the teacher was trying to teach.
i'd argue that i may well have. the best maths professor i had in school focused on teaching how to think through the problems. calculators (even simple 10 funciton calculators) were banned from his classroom. he taught me how to reason through the problem to arrive at the correct solution, he did not teach me 30 formulas that i knew how to apply be rote and i could use to instantly solve any problem that exactly fit the form that the formula needed.
Learning the formulas makes one faster at solving the problems if they conform to the canonical form, but makes no help in solving the problems if they vary from the canonicall form. I learned how to think about the problems analytically so i can handle moth the canonical forms and the variations, albeit not necessarily as fast as someone who has all the solution forms memorized,
-
the best maths professor i had in school focused on teaching how to think through the problems
This is what teaching should be, not rote memorisation to pass exams
-
I think of methods of solving maths problems like design patterns: when the point is to solve the problem in front of you, use whatever works for you, but when you want to talk with other people about how things are designed, it really helps to understand the patterns they prefer to use. So in that sense, you should absolutely learn how the Common Core wants you to add numbers, even if you don't like to use it in real life.
-
not rote memorisation to pass exams
How do you test someone's ability to think through a problem if your test grading policy is "If you get the right answer, it's right, no matter what you did in the process"? Wasn't the whole complaint here against test questions that say "How do you derive this answer to that problem"?
-
you should absolutely learn how the Common Core wants you to add numbers
agreed, but only if the converse it true for the people who use the common core method of adding.
-
How do you test someone's ability to think through a problem if your test grading policy is "If you get the right answer, it's right, no matter what you did in the process"? Wasn't the whole complaint here against test questions that say "How do you derive this answer to that problem"?
That's a tricky issue to solve; upthread, there are two very different, yet equally correct, ways of answering the question, yet they'll likely end up marked differently. And I'm willing to bet my logical deduction method would be marked down in favour of @algorythmics and @CarrieVS algebraic approach, which is unfair, as both methods are equally valid in their conclusions.
-
I think your answer would be marked down not because it isn't the right approach or goes to far, but it doesn't feature any step that maps to N^2 - n - 90 = 0.
-
only if the converse it true
I think as many people as possible should be exposed to as many methods as possible so they can best find the one that suits them :)
That said, each of us can only really control what we learn ourselves. I can't make everyone in the world understand how I think about numbers, but I can try to learn how they think. Even a teacher can only try their best to expose their students to new ideas, they can't force them to learn. So I tend to give advice with that in mind.
I had a hell of a time in math classes at uni because of my dyscalculia. Numbers don't stick in my head as firmly as they should, they kind of blur and shift when I'm not focusing really hard on them. Someone could tell me their phone number is 644-4646 and I'll come away thinking it's 866-6464 instead. So when I had to do long, complex, multi-step math problems, I'd often transpose digits, drop minus signs, or even slip a decimal place in the middle, coming up with the wrong answer but partial credit for knowing how to solve the problem. I'd have loved problems where they told me the answer and tested my ability to solve it, because I'd know when I did something wrong and could go back and revise until I got it right.
I also think the common core "count up" method makes perfect sense. So there's that.
-
Stupidly easy. It's not hard in any way, shape or form.
Seriously.
[spoiler]
1/3 = (6/n) * ((6-1)/(n-1))
1/3 = (6^2 - 6) / (n^2 - n)
(n^2 - n) = 3 * 30
n^2 - n - 90 = 0
[/spoiler]
-
Absolutely; I map from n² - n - 90 = 0 to the probability, and get the same result. So why is my method discouraged?
-
I think the key problem here is the definition of answer. For a lot of people and with good reason the answer is assumed to be "replace all variables and show their values", because for the first 10 years of school that's what you are supposed to do. What is 1 + 1? becomes x = 1 + 1 solve x, except more convoluted.
The problem is, a lot of interesting and more complicated maths (and obviously programming built on top of it) inherently requires you to manipulate equations without solving them.
-
... okay i get that, but it still alloys me that you gave me a word problem followed by "here's the answer to the word problem!
But...that's not what they did. You're answering a question they didn't ask.
-
Stupidly easy. It's not hard in any way, shape or form.
Unless you mix up orange and yellow like I did at first.
