This is a little test of reasoning ability. I would prefer that for the first few days, only ID advocates post answers. These questions, and the underlying reasoning, are widely discussed on the internet, so you may have encountered them. If you have, I would appreciate knowing that fact. Also, for those who have seen them before, I would like to know how you did the first time you encountered them.
If anyone spots a typo or logical error, I’d appreciate hearing about is so it can be corrected.
The answers I’m looking for are in three parts:
First — yes or no — can the puzzles be solved by reason, assuming ordinary knowledge of the vocabulary. There are no tricks or unusual meanings involved.
Second, provide the answer.
Third, the provide the reasoning or proof.
Uncommon Descent frequently invokes logic and reason. this is a challenge to anyone who posts at UD. Feel free to post your answers on this thread or at UD.
Here are the questions:
1. [The original editor has been sacked. Re-Edited to straighten out the mess: The price of a cheeseburger is $2.20, the price of a plain hamburger plus the price of the added cheese.] A plain hamburger costs two dollars more than the added cheese. How much does a plain hamburger cost?
2. In Elbonia, one person in ten thousand has Ebola. A new test is so good that anyone who is infected will test positive. But three percent of uninfected people will also test positive. John, a citizen of Elbonia tests positive. What is the probability that John has Ebola?
3. I have a deck of picture cards. They have automobiles on one side and living things on the other side. I have looked through them, and I think they follow the following rule: if a card has a GM automobile on one side, it will have an animal on the other side. After shuffling, I deal out four cards.
Cat, Ford, Petunia, Chevy
What cards must I turn over to test my hypothesis?
4. William is tweeting Betty, but Betty is tweeting John. William is in love, but John is not. Is a person in love tweeting a person who is not in love?
5. Elbonia has invented a treatment for Psoriasis. During a recent blind test, of the patients who were given the treatment 197 improved and 95 did not.
Of the patients who were given a placebo, 45 improved and 20 did not.
Is the treatment effective?
Possibly related video.
I’ve spotted a couple of types, but don’t have the ability to edit the post.
Check whether you can edit it now.
Thanks. I fixed two small typos that have no effect on the puzzles.
Channeling my inner Mullings…” you are now on strike 1 for schoolyard taunting trollish behaviour, in a context of sustaining willful strawman misrepresenatations that amount to speaking with disregard to duties of care to truth, accuracy and more. Remember, right from the outset you have made false accusations with personal implications; which on being corrected you have evidently willfully not withdrawn. Kindly, clean up your act or I will ask you to leave this thread and others I own. KF”
It didn’t make sense the first time he said this, so I was just hoping that it would make more sense under this context.
I find this question unclear, particularly the “which is two dollars more than the added cheese” bit. If I’m not the only one, you might want to rewrite it.
I also find it unclear. There seems to be an unstated assumption about the relation between the price of a hamburger and the price of a cheeseburger.
But the plain burger costs $2. It’s obvious!
But what if the cheese is an emergent property of the perfectly made hamburger?
If cheese emerges, the hamburger could not have been perfect.
The unstated assumption is that the price of a cheeseburger is the price of a hamburger plus the price of the added cheese. I suppose I’m just old, but there was a time when you were asked if you wanted cheese.
The ontological chef? Essential, not emergent.
As a good capitalist, I would charge more than the marginal cost of the cheese.
I’m all for that, but the question is really about price, rather than cost. I don’t think I will edit the OP just for that.
But I’ll wager the price of a cheeseburger that no one from UD successfully Meets the challenge. Even though a bit of Google-fu will reveal the answers. I changed the words and numbers, so you have to be able to follow the logic.
I think that petrushka is wrong to think that IDers will do bad on these questions. I’d bet a cheeseburger they’ll do just as well as the science/evo people. I’ve gotten them impression that most of the IDers are very smart, and some may be brilliant. Their spectacular lapses in reasoning ability only occur with issues directly relevant to their religious worldview. Most want to believe in a miracle working God, so evoltion is out the window. Most want to believe that the major events in the world, and the ultimate fate of humanity are in Gods hands so climate change can’t be true. Some ( such as Philip Johnson) believe that the Old Testament contains orders from God concerning moral conduct, so HIV doesnt cause AIDS, immoral behavior does.
I don’t mind taking the risk that I will lose.
I will point out, however, that the article from which I lifted these problems asserts that the ability to solve them is not correlated with high IQ.
I like these problems because they are of a type that comes up often in real life. Are medicines effective? Do I have a disease because I tested positive? How does a scientist test a hypothesis? How do I reason about evidence?
They do claim to use math to understand things. Not surprised they’ve not showed up because , erm, some TSZers also post on that site on iniquity, AtBC.
Also, Cowardice.
RodW,
I’ll bet a single-malt cheeseburger that when you wrote, “I’ve gotten the impression that most of the IDers are very smart, and some may be brilliant,” you were not thinking of the UD crowd.
I asked JoeG about the hamburger one, and he said you just have to ask the seller how much a plain burger is, and Joe is not selling any burgers so why are you asking him and anyway, we can’t work it out from the given information alone – the vendor might charge 10 cents for the burger for all we know or give it to you for free because it was a nice day.
Or that you might have been the millionth customer and got it for free plus a million dollars on top, so then it cost –
2.20 in total, there’s just no way to know really.
I did clarify the problem, for those who don’t remember how cheeseburgers and hamburgers used to be priced.
So you’re admitting to rewriting history, you despicable Darwinist!
I edited the problem and noted the edit in bold. I’m a little rusty in math. I took first year algebra 55 years ago. It would be a rather simple word problem in first year algebra. Or maybe second, but I doubt it. Kids are being given these kinds of problems earlier now. And parents are having fits.
My “clarified” version is:
The price of a cheeseburger is the price of a hamburger plus the price of the added cheese. A cheeseburger costs $2.20, which is two dollars more than the added cheese. How much does a plain hamburger cost?
I’m not smart enough to make these problems up, and I tried to keep the phrasing parallel to the originals. I have solved the “love/tweet” kind of problem, I find those to be very difficult. I think I have now figured out how to attack them. There’s one in the first Harry Potter book that has seven statements rather than three.
They are supposed to be difficult, but I think anyone who claims to have found the flaws in mainstream science or mathematics should be able to solve them and be able to show the step by step reasoning.
How about it Barry? Mung? Gpuccio? Kariosfocus? BA77? Uprightbiped?
I found (2) and (5) the easiest, and I think I’ve solved (3). But to make (3) work as a puzzle, there has to be an implicit restriction that you can only turn over three cards, right?
For some reason, though, I can’t set up (1) correctly in my head. I want to treat it as a simple arithmetic problem and that the hamburger is $2.00, but that can’t be right (can it be?). Anyone willing to explain where I’m going wrong, or give me a hint in setting it up correctly?
KN,
Try setting it up as a system of two equations, one dealing with a sum, and one dealing with a difference.
The key word in the card problem is “must.” Which are obligatory for testing the hypothesis?
I don’t want to give anything away until the UDenizens have had a good long shot at the puzzles. I think if any of them were up to it, they would have spoken up by now. But I want to make sure they know about it.
I find most of them to be hard. The point made by the original author is that the solutions seem counterintuitive until they are done step by step.
I have already mentioned algebra. Most of them can be translated into algebraic statements. Not much different from the dreaded two cars travelling in opposite directions problem.
I’m betting that the UDers — especially Joe — will not drink it, even after being led to the water.
petrushka,
I’m Thinking, Fast and Slow, about these problems.
KN:
“I found (2) and (5) the easiest, and I think I’ve solved (3). But to make (3) work as a puzzle, there has to be an implicit restriction that you can only turn over three cards, right?”
I don’t see that.
You have to turn over the Chevy card. If it has anything not animal on the other side, that disconfirms the hypothesis. You have to turn over the Petunia card. If it has a GM vehicle on the other side, that disconfirms the hypothesis.
But turning over the Ford card won’t tell you anything about the GM-animal linkage, no matter what’s on the back of the Ford card.
And turning over the Cat card isn’t a good test of the hypothesis, IF it has a GM vehicle on the other side, fine, but observing one single instance of apparent GM-animal link isn’t very useful: could be sampling bias, could be coincidence. Meanwhile if it has a non-GM vehicle on the other side, that;s not useful either. Because there’s nothing (in the way that the problem is stated) which indicates that the animal-GM link is exclusive. Maybe all GM vehicles must be linked to animals, but maybe other brands are also linked to animals, at least sometimes.
Okay, but UD just got the challenge, so give them a few days.
There’s no disgrace in finding the problems hard. They wouldn’t have been published if they weren’t hard. The disgrace is in asserting you are smarter than Cantor and Einstein without being able to solve eighth grade word problems.
Hotshoe, with your permission I’d like to (temporarily) remove your solution.
KN,
I cannot find the details of where I read it (perhaps it was Thinking Fast and Slow), but I think studies have found that people do much better at solving (3) when it is posed in a social context, rather than using abstractions like playing cards. For example, as I recall, people do much better when it is posed about whose ids and whose drinks you have to check to find underage drinkers in bar.
Maybe that says something related to Brandom, maybe not.
In your case, perhaps this helps: which card would a logical positivist turn over first? Which would Popper turn over first?
That would be 1953.
I cannot find the details of where I read it (perhaps it was Thinking Fast and Slow), but I think studies have found that people do much better at solving (3) when it is posed in a social context, rather than using abstractions like playing cards. For example, as I recall, people do much better when it is posed about whose ids and whose drinks you have to check to find underage drinkers in bar.
I think it was Kahneman and Tversky who discovered that in the 1970s. So you would have been familiar with that from Kahneman’s recent book.
Maybe that says something related to Brandom, maybe not.
No, Kahneman’s work is far too empirical for Brandom! 🙂
Petrushka:
That would be 1953
Yes, it was good advice then and it’s good advice now!
Spoiler alert; advice below.
——————
“Check your work!”
In this case, plug in your answer and see if it works. I think most people see an obvious answer and stop there. At least, that’s what I did. I’m going to claim most people make the same mistake to preserve my self esteem.
(If this post spoils the intent of your OP, feel free to delete it. )
Petrushka, sure, put my solution somewhere invisible; sorry for posting soon than I ought to have.
Oops, “sooner” not “soon”
My kingdom for an Edit button 🙂
This is why you’re in a higher pay grade than me. I will fix it again.
BruceS:
Or do as I do, and stop when the wording looks right. My only defence in the first problem is that I anticipate my own fallibility and asked for proofreading.
Petrushka: “I want to ask some math questions that I looked up online, which I really struggled with understanding and got the answers from someone else, and then I want to post them as a challenge to Id’ists to show how stupid they are. But first I want to demonstrate my pathetic grasp of the English language by completely mangling the questions so badly that my own stupidity becomes one of my tools for showing how dumb they are. Can you please take my challenge now so I can confirm how brilliant I am?”
Just switched comment editing back on. Thought it might help in managing spoiler comments!
@ phoodoo
Wouldn’t the best way to respond to petrushka to be to give answers to the puzzles and thus show at least one ID-proponent is not dumb?
ETA
Happy New Year everyone.
phoodoo,
If the answers are online, then free free to give them!
I need no further evidence of your brilliance then your comments on the “Is zero even” thread at UD.
It’s all just silly diagrams on paper really!
Cantor proved nothing with his proof?
On second thought, don’t attempt any of the puzzles in this thread. There’s really no need!
There’s no point in trying to have an intellectual discussion with people incapable of abstract reasoning.
[Phoodoo at UD?]
“… there is no reason to insist on pairing things up the way he does, as if its the only way. Furthermore, its just a silly diagram on a piece of paper, I could place all the numbers with curly shapes on one line, and numbers with straight lines on the other, it is just as meaningful.”
reminds me of an historically-easy puzzle.
Given this diagram :
A . . . E F
__________
. B C D
find the digital value of WSN and XTQ
Yes, it has one solution. Yes, it’s logical, (although it doesn’t have anything to do with Cantor’s math, or math at all, really). Yes, it’s literally just a “silly” diagram …
No prizes for solving it, but a big smiley!
Phoodoo:
Of course I am not the one claiming to be smarter than Cantor and Einstein. That honor belongs to the regulars at UncommonDescent.
I merely think that anyone claiming to be smarter than Cantor should be able to do first year algebra, or to notice that a problem is unsolvable as written. (Step one of my challenge,remember?)
By agreeing with Keiths that the first problem was incorrectly stated, you are admitting he is correct. Which he is at UD, also.
Petrushka,
“See, Keiths was right that I don’t have even elementary level English skills. See how smart he is!”
Haha, I guess compared to you, he is a freaking genius.
Kantian Naturalist
“There’s no point in trying to have an intellectual discussion with people incapable of abstract reasoning.”
Kantian, Oscar Wilde you are not.
That’s a distinct possibility, but it has nothing to do with the observed fact atha there are people at UD who claim to be smarter than Cantor, and people claiming to be smarter than Einstein, but who cannot do simple logic or first year algebra.