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Re: Re: Re: Re: Re: Re: Smart?

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Originally posted by drizzt81 oops today isn;t my day, i was thinking that i had to DETERMINE the weight of yours.. not balance it.. with a sum of 52 i will be able to tell you how much your weight is :/ still not bad, if that had been teh question try 1,3,7,17,31,79

I don't follow. If I give you a 100 weight, how can you tell me that it's 100 if your weights sum to 52?

Your 6 weights work, but are suboptimal :-)

Re: Re: Smart?

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Originally posted by AndiH What's the "worst case"?

The "worst case" depends entirely on your algorithm. For example, if you decided to drop from 1, then 2, then 3, etc... then your worst case would be the 100th floor. It would take 100 tries in the worst case then. You need an algorithm whose worst case is minimal.

Re: Re: Re: Smart?

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Originally posted by Flyboy217 The "worst case" depends entirely on your algorithm. For example, if you decided to drop from 1, then 2, then 3, etc... then your worst case would be the 100th floor. It would take 100 tries in the worst case then. You need an algorithm whose worst case is minimal.

No, in that case my worst case would be 99 since you said that the egg would break if dropped from the 100th floor. Also, now I assume that there's no ground floor?

Re: Re: Re: Re: Smart?

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Originally posted by AndiH No, in that case my worst case would be 99 since you said that the egg would break if dropped from the 100th floor. Also, now I assume that there's no ground floor?

You are correct, 99 is the worst case, since I've implicitly guaranteed you it will break by 100 (by enforcing that you must actually find N, rather than allowing you to say "it doesn't break from 1-100"). It's a moot point though; it doesn't change the optimal algorithm or final answer.

Not sure what you mean by a "ground floor." The eggs may break from story 1, if that's what you mean.

Re: Re: Re: Re: Re: Re: Re: Smart?

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Originally posted by Flyboy217 I'll go one step further and tell you that you make a faulty assumption in your first sentence. Any more and I'd be telling you the solution.

Ok, I think I've figured it out.

You drop the first egg at the 15th floor. If it breaks, you count up in sequence from 1 to 13 (14 drops).

Then you drop the next egg at the 29th floor. If it breaks, count up in sequence from 16 to 28 (again 14 total).

Keep going up to the 42nd, 54th, 65th, 75th, 84th, 92nd, and 99th floors, which gives you intervals of 11, 10, 9, 8, 7, etc. respectively, all with a total worst-case drop of 14.

So the worst case is 14.

Right?

I'd hardly call this an "elegant" solution though... it's not elegant unless you know it in advance.

I still think there's something wrong with your question 3. The cups are in arbitrary positions, and the "genie" can rotate them at an arbitrary angle, and you're saying there's a way to guarantee getting them all face up?

There has to be something in this question that's not random, aside from your instructions. That is, unless we're talking about a Gaussian system and assuming an infinite number of "rounds"...

Re: Re: Re: Re: Re: Re: Re: Re: Smart?

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Originally posted by DigiNut Ok, I think I've figured it out. You drop the first egg at the 15th floor. If it breaks, you count up in sequence from 1 to 13 (14 drops). Then you drop the next egg at the 29th floor. If it breaks, count up in sequence from 16 to 28 (again 14 total). Keep going up to the 42nd, 54th, 65th, 75th, 84th, 92nd, and 99th floors, which gives you intervals of 11, 10, 9, 8, 7, etc. respectively, all with a total worst-case drop of 14. So the worst case is 14. Right? I'd hardly call this an "elegant" solution though... it's not elegant unless you know it in advance.

The worst case is indeed 14, but your solution is slightly flawed. Suppose the eggs break at 15. Then you try 15, find the egg breaks, and try 1-13 and it doesn't. You don't know whether the answer is 14 or 15 now. Instead, your first drop should be 14.

It extends nicely so that an M-story building requires N drops such that N(N-1)/2 = M. The fun part is understanding that your drops must decrease to balance out the worst case. Most people wrongly believe it must be constant. I sadly removed that joy for you :-P

When I'm in the mood for extra math homework, I'll find you.

Until then... I'll just wait for Acid Junkie to have a go.

quote:

Originally posted by DigiNut I still think there's something wrong with your question 3. The cups are in arbitrary positions, and the "genie" can rotate them at an arbitrary angle, and you're saying there's a way to guarantee getting them all face up? There has to be something in this question that's not random, aside from your instructions. That is, unless we're talking about a Gaussian system and assuming an infinite number of "rounds"...

It is solvable as stated. Feel free to assume an unbounded number of rounds if you like, but please don't try to argue that a random solution will eventually work; it's not *guaranteed* to win.

P.S. I love your pseudo-math terminology. "Real integral" number systems in the "2+2=5" thread. "Directional unit vectors" while trying to explain an n-dimensional space. All that's required of the vectors is that they're linearly independent-- they certainly don't need to be unit, and "directional" is meaningless in this context.

It sounds like you're trying to impress TAs, so I won't burst your bubble. I suppose for the most part, it seems to be working ;-)

i direct your attention to 'writing against your life' by richard mitchell, better known as the grammarian.

i love math just as much as the next guy, but uhh.... well, just read it, especially you intellects. you know who you are. it'll kick your asses to infinity and back before you can say 'MENSA!!!'

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Originally posted by Abject Silver i direct your attention to 'writing against your life' by richard mitchell, better known as the grammarian. i love math just as much as the next guy, but uhh.... well, just read it, especially you intellects. you know who you are. it'll kick your asses to infinity and back before you can say 'MENSA!!!'

I couldn't find this title on Amazon. Is it an older book? What's it about?

And I love the way people associate Mensa with "genius." There are societies with *much* higher intelligence requirements (Triple Nine, Iquadrivium) for truly brilliant people :-)

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Originally posted by Flyboy217 P.S. I love your pseudo-math terminology. "Real integral" number systems in the "2+2=5" thread. "Directional unit vectors" while trying to explain an n-dimensional space. All that's required of the vectors is that they're linearly independent-- they certainly don't need to be unit, and "directional" is meaningless in this context.

Refer to my post in the other thread, I think you're full of shit. FYI, several people here know that I'm finishing up my electrical engineering degree, but I suppose that's not up to your high standards. If you like, we could compare intellectual credentials, but frankly, I think it's a colossal waste of time.

Thank you for insulting me though, because I'm no longer motivated to think about any of the questions you posted, and therefore, you've saved me a lot of time that could be better spent.

Edit: I was just thinking how quaint it is that you elected not to pay any attention to my response to your nonsensical garbage in the other thread, but rather continue to harp on me in this one. Well done, you've made my list of biggest pricks on TA.

This is why I prefer to hang around dumb people a lot of the time... it's so sickening being around someone who's always trying to prove their intellectual superiority. I wasn't insulting you personally with any of my comments in this thread, I simply think that you've worded some of the questions poorly.

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Originally posted by DigiNut Refer to my post in the other thread, I think you're full of shit. FYI, several people here know that I'm finishing up my electrical engineering degree, but I suppose that's not up to your high standards. If you like, we could compare intellectual credentials, but frankly, I think it's a colossal waste of time. Thank you for insulting me though, because I'm no longer motivated to think about any of the questions you posted, and therefore, you've saved me a lot of time that could be better spent. Edit: I was just thinking how quaint it is that you elected not to pay any attention to my response to your nonsensical garbage in the other thread, but rather continue to harp on me in this one. Well done, you've made my list of biggest pricks on TA. This is why I prefer to hang around dumb people a lot of the time... it's so sickening being around someone who's always trying to prove their intellectual superiority. I wasn't insulting you personally with any of my comments in this thread, I simply think that you've worded some of the questions poorly.

I just got around to reading your reply in that post. You claim "...which would not be possible if they weren't unit vectors." "Unit" only means they have a magnitude of one. They are able to describe a linear space regardless of their (non-zero) magnitude.
For more, see http://mathworld.wolfram.com/VectorSpaceBasis.html

As for the "real" and "integral," while I'm sure you understand their mathematical definitions, I'm sure you also understand that they bear no relevance to the question asked.

But that's not what I mean to discuss. I am sure that you, too, are smart. But because your posts are loaded with words like "ludicrous" and "laughable" in regards to other people's questions and ideas, I indeed felt the need to call your bluff. If I misinterpreted your intentions, I apologize. Perhaps I was mistaken in detecting a self-righteous undertone in your posts.

Anyway, sorry to have made your "biggest pricks" list. Hope you'll still think about the problems even if you don't respond.

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Originally posted by Flyboy217 I just got around to reading your reply in that post. You claim "...which would not be possible if they weren't unit vectors." "Unit" only means they have a magnitude of one. They are able to describe a linear space regardless of their (non-zero) magnitude. For more, see http://mathworld.wolfram.com/VectorSpaceBasis.html As for the "real" and "integral," while I'm sure you understand their mathematical definitions, I'm sure you also understand that they bear no relevance to the question asked. But that's not what I mean to discuss. I am sure that you, too, are smart. But because your posts are loaded with words like "ludicrous" and "laughable" in regards to other people's questions and ideas, I indeed felt the need to call your bluff. If I misinterpreted your intentions, I apologize. Perhaps I was mistaken in detecting a self-righteous undertone in your posts. Anyway, sorry to have made your "biggest pricks" list. Hope you'll still think about the problems even if you don't respond.

I explained the relevance to the question asked. If you choose to ignore it or discount it, I can't stop you. Referring to it as "calling my bluff", however, makes me have to laugh at you calling me "self-righteous" in the same paragraph. It's hard to swallow a backhanded apology like the one you're presenting to me.

Yes, any 3 LI vectors can describe "a" linear space, but not THE linear space, i.e. the physical world. For that, you need 3 independent and infinitessimally small vectors, which I perhaps mistakenly called "unit" vectors, but could think of no other appropriate word to describe their magnitudes. What would you call them?

Having said that, even if my post in the "2+2" thread was blatantly incorrect and irrelevant (which it wasn't), it would have still hardly warranted you bringing it into ANOTHER THREAD which had NO RELATION to the former one. Because I use the word "ludicrous" in one thread, it's a reason for you to quote something totally unrelated from another thread which you think is wrong? And not just one thread, but two separate threads. Please, there's no legitimate excuse for doing that.

Don't try to imply that I'm just on here trying to sound smart, because I can dig up a lot of posts where you do the exact same thing. I'm not here to impress anyone, in fact I'm rather PO'ed at myself lately for posting so much in the chillout room, because usually I limit myself to the Toronto forum and just talk about the events and the scene and the other random crap that goes on in there.

You sound like a smart guy and I'm sure we'd be better off as friends than enemies (for what that's worth on the internet). I have no intention of starting a war with you, but I do feel the need to defend myself because this isn't the first time you've harped on me for no particular reason (i.e. the drunk driving lawsuit thread). So let's drop all of this, and continue on with our lives.

Now... back to your regularly scheduled programming.

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Originally posted by Flyboy217 And I love the way people associate Mensa with "genius."

OT: I associate Mensa with FOOD! It's where you go in german universities to get lunch, aka. the cafeteria.

oops, I guess i walked in on a little argument :/ sorry lads

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Originally posted by Flyboy217 I couldn't find this title on Amazon. Is it an older book? What's it about? And I love the way people associate Mensa with "genius." There are societies with *much* higher intelligence requirements (Triple Nine, Iquadrivium) for truly brilliant people :-)

how about the giga society?


and it's a speech.

http://www.sourcetext.com/grammarian/the-booklets/1.htm

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Originally posted by DigiNut I explained the relevance to the question asked. If you choose to ignore it or discount it, I can't stop you. Referring to it as "calling my bluff", however, makes me have to laugh at you calling me "self-righteous" in the same paragraph. It's hard to swallow a backhanded apology like the one you're presenting to me. Yes, any 3 LI vectors can describe "a" linear space, but not THE linear space, i.e. the physical world. For that, you need 3 independent and infinitessimally small vectors, which I perhaps mistakenly called "unit" vectors, but could think of no other appropriate word to describe their magnitudes. What would you call them? Having said that, even if my post in the "2+2" thread was blatantly incorrect and irrelevant (which it wasn't), it would have still hardly warranted you bringing it into ANOTHER THREAD which had NO RELATION to the former one. Because I use the word "ludicrous" in one thread, it's a reason for you to quote something totally unrelated from another thread which you think is wrong? And not just one thread, but two separate threads. Please, there's no legitimate excuse for doing that. Don't try to imply that I'm just on here trying to sound smart, because I can dig up a lot of posts where you do the exact same thing. I'm not here to impress anyone, in fact I'm rather PO'ed at myself lately for posting so much in the chillout room, because usually I limit myself to the Toronto forum and just talk about the events and the scene and the other random crap that goes on in there. You sound like a smart guy and I'm sure we'd be better off as friends than enemies (for what that's worth on the internet). I have no intention of starting a war with you, but I do feel the need to defend myself because this isn't the first time you've harped on me for no particular reason (i.e. the drunk driving lawsuit thread). So let's drop all of this, and continue on with our lives. Now... back to your regularly scheduled programming.

Wow. My apologies, Digi. After reading this post, I can't deny that you're a mature, thoughtful guy. I also didn't intend to turn this into a war, although I guess it looks as though I was trying to make it one. I had no reason to post those responses in two different threads. That thread had sunk to page 2 where it seemed like you weren't going to read it, and I was already talking to you in this thread.

As for the drunk driving thread... hehe, I didn't even realize that was you. I'm not one for launching campaigns against people, especially in online forums. (By the way, I just re-read that thread, and I'm only trying to debunk your position, not make a personal attack).

I often hear people break out meaningless big words to either make themselves sound smart or make others sound stupid. Usually, it upsets me when I see this. I've misjudged you on both of those, so I apologize. I, too, would rather see us friends than enemies.

Please accept this as a sincere apology, and please try out the problems cuz they really are fun .

P.S. I'd like to explain where I was going with the "real integral" and "directional vector" posts, sans any personal implications.

The integral number system is necessarily real. But more importantly, the whole question of "when is 2+2=5" depends only on the meaning of the symbols themselves. It's safe to assume that "+" and "=" have their usual meanings. The base is of no importance, since, as you pointed out, "2" and "5" are digits. That said, one could easily come up with different values for those numerals to make the equation true. This can be said regardless of the type of number system (i.e., real, complex, integral, rational, etc...).

For the linear algebra discussion, the vectors don't need to be unit or infinitesimal to describe any linear space, including the "real" one (as you know, ALL n-dimensional linear spaces are isomorphic). If we use a unit vector basis, and we have a point at {x, y, z), then scaling our basis vectors up by N will only change our point's representation to (x/N, y/N, z/N). This is what I meant by "regardless of their magnitude." As long as our basis vectors are non-zero (and they are, by definition), any point can be described as a linear combination of them (they "span" the space). This is a nice result of the spaces being isomorphic.

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Originally posted by Flyboy217 For the linear algebra discussion, the vectors don't need to be unit or infinitesimal to describe any linear space, including the "real" one (as you know, ALL n-dimensional linear spaces are isomorphic). If we use a unit vector basis, and we have a point at {x, y, z), then scaling our basis vectors up by N will only change our point's representation to (x/N, y/N, z/N). This is what I meant by "regardless of their magnitude." As long as our basis vectors are non-zero (and they are, by definition), any point can be described as a linear combination of them (they "span" the space). This is a nice result of the spaces being isomorphic.

Alright, now that I think about it, you're right on that. For some reason I was assuming integer coefficients... can't imagine why.

Anyway, all's well that ends well, so let's get back to the problems. Has everybody else given up?

fuckin nerds!

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Originally posted by Abject Silver how about the giga society? and it's a speech. http://www.sourcetext.com/grammarian/the-booklets/1.htm

Just read it. Don't know how to respond .

Anyway, yeah... the paths to these problems are well-worn, and they won't reveal any new insights to humanity. But you gotta start somewhere, and they're fun

ok how is the first building one not log n??

first of all, is N unique to both eggs or each egg has its own different height? cuz it doesnt really say, if it is not unique, then its logn of each...

taking worse case, log[base2] n = 8 ..*2 = 16 which is the right answer

the genie one, u can just do anything and assume at inf it will work out???? i dunno

and the coin one depends on the coins you choose.... it asks for the most expensive u can buy with exact change?? so if u pick coin A = 10^10 $ then thats more expensive than a lower denomination

edit* ok i read the question wrong, but it still depends on the coins, for instance, if u pick 2,3, then most expensive is 1$ cuz anything after that u have exact change for, now if u pick 10$ and 9$ u can buy 11$ and u wont have exact change, but 11>A>b , but in first case 1$

Re: Smart?

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Originally posted by Flyboy217 4a) Prove that any set of 10 integers from [1, 1000] must contain two distinct subsets each with the same sum of elements. [5 min]

question about this one:
what do you mean by "sum of elements?"

say we use this set:
SETA {1,2,3,4,5,6,7,8,9,10}

now we can create two subsets:
SUBA {2,3}
SUBB {5}

which both sum to be 5. Is that what you mean? Sorry, but I cannot go about solving the problem if I don't understand the lingo... :/

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Originally posted by Resnick ok how is the first building one not log n?? first of all, is N unique to both eggs or each egg has its own different height? cuz it doesnt really say, if it is not unique, then its logn of each... taking worse case, log[base2] n = 8 ..*2 = 16 which is the right answer

Res bud, that one's already been answered! Read back a few posts.

Re: Re: Smart?

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Originally posted by drizzt81 question about this one: what do you mean by "sum of elements?" say we use this set: SETA {1,2,3,4,5,6,7,8,9,10} now we can create two subsets: SUBA {2,3} SUBB {5} which both sum to be 5. Is that what you mean? Sorry, but I cannot go about solving the problem if I don't understand the lingo... :/

I'm pretty sure that's what it means. Those are both subsets, with the same sum, except that the set you picked has far *more* than two subsets with that some. You only need to prove that there's at least two.

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Originally posted by DigiNut Res bud, that one's already been answered! Read back a few posts.

ya i know, but they said the answer is 15...which i dont see how it can be

edit BWAHHAHA sorry ive done too much programming, the answer is 14, but thats because u can use elimination to say that u dont have to test the last case, because it has to be that..so u can just assume its that...where in, say java u still have to do it..my bad

but the answer is log[base 2] of 100, u just multiply by 2 since theere are 2 eggs

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