So I was sitting in the WashU library reading my Evidence assignment for the first day of class, and I encountered a section on inductive and deductive reasoning. As examples of deducting reasoning, the textbook gave two problems without answers. I read the problems, and just ran into brick walls. Like headfirst, just plowed right into them and could not move an inch. I sat there and thought over them, and re-thought over them, and felt that sick feeling where your mind simply refuses to budge. Like I was dividing by zero, ya know? DOES NOT COMPUTE! ERROR! Drove me fucking insane.
So, after awhile, I just gave up...but I refused to look on the internet for a solution. Because I would not let it beat me. I didn't want to cheapen it. I did not want to simply skip past it. Instead, I took a nap with AHJ for two hours. As I came out my nap and laid there in the dark, the stupid problems were still in my head, and I felt like I was on the cusp of it....but I could NOT figure it out. Everytime I thought I had solved it, I skated on the edge of a solution but could simply not see it. Driving me crazy. So I went outside, smoked a cigarette and just thought about it. And then I got it. And once I got it, I tried again on the second one, and I got that one too. So, basically, it took me four hours. But I was ecstatic that I had overcome it.
So, for the hell of it, I've decided to reproduce these problems and post them for you. So, all I ask is that you don't look the answers up...if you respond to this at all.
1) Once upon a time in a faraway land, the king wanted his son to marry the smartest young woman in the kingdom. Three tied for the highest score. The king seated these three women at a round table. He asked them to close their eyes, which they did. He then announced that he was placing a beanie on each of their heads, positioned in such a way that, when they opened their eyes, each would be able to see the beanies on the heads of the other two but would not see the beanie on her own head. The king told the young women that the beanies might be either red or white. "When you open your eyes, you are to raise your right hand if you see one or more red beanies. When you deduce the color of the beanie on your own head, lower your hand and rise. Now open your eyes." The king had, in fact, placed red beanies on each of the three women's heads. All three raised their hands. After ten seconds, one of htem lowered her hand, rose, and explained her deduction that she was wearing a red beanie.
How did she do it?
2) In a faraway land there were two tribes. The Lynx were inveterate liars, while the Cougars were unfailingly veracious. Once upon a time a stranger visited the land, and on meeting a party of three inhabitants inquired as to which tribe they belonged.
The first murmured something the stranger did not catch. The second remarked, "He said he was a Lynx." The third said to the second, "You are a liar."
What is the tribe of the third person?
11 comments:
2)
If first person was a Lynx, he wouldn't say he was a Lynx (b/c he is a liar)
If first person was a Courgar, he wouldn't say he was a Lynx (b/c he is truthful
Thus, second person has to be lying and the third person has to be a Cougar (b/c he truthfully pointed this out)
DA
(still working on first one)
1)
Only two possible scenarios from each girl's perspective since they all view two red beanies.
1) Everyone is red
2) The other two are red but I am white.
From A's perspective, if she is white, B raises hand for C and C raises hand for B.
From B's perspective, if she is white, A raise hand for C, and C raises hand for A.
From C's perspective, if she is white, A raises hand for B, and B raises hand for A.
In other words, no matter which perspective you look through, each girl must be red for this to cumulatively work (each girl is depended on to be red for this to work in cum from all perspectives).
(not sure if this is a satisfactory answer but I have to get to work)
DA
You two are so much a like it's scary :) Glad we all got to hang out this weekend...
the first one's easy: no one else stands up.
it was good seeing everyone this weekend.
j
1) Yes, the Lynx Cougar answer is correct.
2) I don't think Mr. DA Colon's answer is correct for the beanies, since it only takes the sight of 1 red beanie for each person to raise their hand.
3)I think this may be correct...but can you elaborate?
I agree...I still don't really understand the first one...Adm-can you explain it?
DA
You mean explain the answer? Or the question?
The question itself is just copied down verbatim from my textbook. The trickiness of it is that the king says "raise your hand if you see ONE or MORE red beanies" meaning that if the girl who figured it out is wearing white, each of the three girls would still see at least one red beanie.
The problem is supposed to be one of deduction, an airtight logical proof. I have an answer, which took the form of a bumbling, rambling statement...but eventually made sense and became coherent...and I hope it's the right answer, because I can't imagine trying to figure out another one. (it's pretty much an explanatory version of "j's" answer.) That or I'd throw myself off a building in mounting frustration.
Hey-fuckin-fantastic!
...Turns out I didn't even need to read through that section for my Evidence class. Looks like they assigned everything EXCEPT that page.
How am I supposed to be a gunner if they take away my opportunities?
I think reading an unassigned page, fretting over the answer, discussing it w/friends, and posting it on a blog = gunnerism (dont you worry :))
yeah,.. there should totally be a blog about this blog.
j
Well...I'm just gonna post what I think the answer is...although I think J got it.
From the Perspective of A: If A is wearing a white beanie...
--Then girl B would look around and see that girl C is wearing a red beanie, and girl A is wearing a white beanie. And the only way that girl C could be raising her hand is if girl B is also wearing a red beanie. Thus, girl B would KNOW she is wearing a red beanie and identify the color of her hat.
Thus, since Girl B has not identified her own beanie as red after 10 seconds, A's beanie cannot be white…thus it must be red. So, yes, to J, since no one else identified their beanies, A's beanie must be red.
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