EPTHappy 410th Birthday, Fermat! - Page 2
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intotheheart
Canada33091 Posts
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EsX_Raptor
United States2802 Posts
Assume that we have the following string: MI and that we can perform operations on it based strictly off the following rules: I. Add a U to the end of any string ending in I. For example: MI to MIU. II. Double any string after the M (that is, change Mx, to Mxx). For example: MIU to MIUIU. III. Replace any III with a U. For example: MUIIIU to MUUU. IV. Remove any UU. For example: MUUU to MU. Is it possible to obtain MU? If you find an answer to this, please post it in spoilers. I'm still working on it! Edit: New page: More decoration: ![[image loading]](http://www.mathfail.com/optical-illusion2.jpg) | ||
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SecondChance
Australia603 Posts
 I understand to an extent, but it looks like this: <|understood|-----lolwut---------------------------------------------------------------------------------------------------------|> | ||
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ComaDose
Canada10357 Posts
On August 18 2011 00:37 SecondChance wrote: + Show Spoiler + All those who didn't go so well in highshcool and have no fucking idea what is going on in this thread yet wished they understood say "I". I understand to an extent, but it looks like this: <|understood|-----lolwut---------------------------------------------------------------------------------------------------------|> You wont learn this in any high-school I've heard of. I spoiled myself with a solution to the MI string from google lol . I want more decoration! | ||
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EtherealDeath
United States8366 Posts
On August 18 2011 00:35 EsX_Raptor wrote: Let's do the good-old MU Puzzle: Assume that we have the following string: MI and that we can perform operations on it based strictly off the following rules: I. Add a U to the end of any string ending in I. For example: MI to MIU. II. Double any string after the M (that is, change Mx, to Mxx). For example: MIU to MIUIU. III. Replace any III with a U. For example: MUIIIU to MUUU. IV. Remove any UU. For example: MUUU to MU. Is it possible to obtain MU? If you find an answer to this, please post it in spoilers. I'm still working on it! Edit: New page: More decoration: + Show Spoiler [solution] + We approach this algebraically. Suppose we have n Is, and we want to reduce them to a single U. We approach this instead as k+3 I's, since the first 3 I's we can reduce to a U. The question is then, given what k can we completely erase the string. The only way we can remove strings is to remove UU. UU is produced by k=6. Thus, in order for the string subsequent to M to be reducible to U, it must consist of 3+6n I's, for some n. At the same time, we can only generate powers of 2 for the number of I's. Thus 3+6n = 2^m for n,m, which is so say we want an m such that 2^m - 3 ≅ 0 mod 6. 2^1 ≅ 1 mod 6 2^2 ≅ 4 mod 6 2^3 ≅ 2 mod 6 2^4 ≅ 4 mod 6 etc we have hit a cycle Therefore it is impossible to produce MU. Other cases ignored because it is clearly impossible to reduce them. edit - Aw fuck it according to wiki I could have just used invariants LOL so much simpler fml. | ||
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EsX_Raptor
United States2802 Posts
On August 18 2011 01:57 EtherealDeath wrote: + Show Spoiler [solution] + We approach this algebraically. Suppose we have n Is, and we want to reduce them to a single U. We approach this instead as k+3 I's, since the first 3 I's we can reduce to a U. The question is then, given what k can we completely erase the string. The only way we can remove strings is to remove UU. UU is produced by k=6. Thus, in order for the string subsequent to M to be reducible to U, it must consist of 3+6n I's, for some n. At the same time, we can only generate powers of 2 for the number of I's. Thus 3+6n = 2^m for n,m, which is so say we want an m such that 2^m - 3 ≅ 0 mod 6. 2^1 ≅ 1 mod 6 2^2 ≅ 4 mod 6 2^3 ≅ 2 mod 6 2^4 ≅ 4 mod 6 etc we have hit a cycle Therefore it is impossible to produce MU. Other cases ignored because it is clearly impossible to reduce them. That's what I thought. Whoever made that puzzle made me spend quite some time trying to solve the unsolvable. lol By the way, it's your turn to ask us a question! | ||
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EtherealDeath
United States8366 Posts
On August 18 2011 02:05 EsX_Raptor wrote: That's what I thought. Whoever made that puzzle made me spend quite some time trying to solve the unsolvable. lol By the way, it's your turn to ask us a question! Hmm... Explain why the following scenario is true. Suppose we have two entangled particles, let's say their state is a|1>|0>+b|0>|1> to be simple, where the values of a and b are not particularly important save that their squares sum to 1, but let's use one of the Bell States, that is a=b=1/sqrt(2). Now we measure one of the particles to determine it's actual state. We know that instantaneously, the state of the other particle is set. However, it is impossible to determine any classical information from this instantaneous effect - i.e., cannot gain any physical information. Why? Or rather, what information do you think you could gain that you didn't have before? | ||
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TL AntiHack
39 Posts
On August 18 2011 00:21 IntoTheheart wrote: Best blog ever. Just sayin'. | ||
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EtherealDeath
United States8366 Posts
On August 18 2011 02:17 TL AntiHack wrote: 5/5, you sir deserve applause. Thank you for making my day better. hax. | ||
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Pengtoss
207 Posts
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Aletheia27
United States267 Posts
On August 17 2011 23:49 Iranon wrote: Oh, right! And it sure would -- for number theoretic reasons. It would allow for a fast factoring algorithm, which compromises RSA. I'll keep on the topic of fun math that a lot of people know about but relatively few actually follow. Can you turn a sphere inside out without poking holes in it or making any sharp creases? The sphere's surface can pass through itself, and you can stretch and rotate parts of it as much as you like, but you can't break it and glue it back together. If you know what the terms mean, I'm asking for a diffeomorphism between two spheres that reverses the orientation. I believe you can although it hinges on the axiom of choice... EDIT: I don't remember exactly why though... Guess I wasn't meant to be a math major | ||
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Primadog
United States4411 Posts
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Ruyguy
Canada988 Posts
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Kukaracha
France1954 Posts
But then I grew up and found out that I missing out a whole beautiful world... I don't know if I'll ever dedicate myself to it but I'd like to give a try oince more, by myself this time. | ||
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ComaDose
Canada10357 Posts
I only took first year chemistry and promptly forgot everything involved. I only mention chemistry becuase i only vaguely recognize the syntax involved in "a|1>|0>+b|0>|1>" as from that class moar math and physics! I propose a new question: "whoes 410th birthday is it and what is he famous for?" should be easy enough. | ||
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Aletheia27
United States267 Posts
On August 18 2011 04:06 ComaDose wrote: EtherealDeath's question was too hard! I only took first year chemistry and promptly forgot everything involved. I only mention chemistry becuase i only vaguely recognize the syntax involved in "a|1>|0>+b|0>|1>" as from that class moar math and physics! I propose a new question: "whoes 410th birthday is it and what is he famous for?" should be easy enough. It's a quantum physics problem actually.... but i don't want to answer this cause I don't havea good question  | ||
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EsX_Raptor
United States2802 Posts
By the way, I have been practicing writing trivial proofs and decided to give proving the MU puzzle a try: ![[image loading]](http://i56.tinypic.com/20kf7m0.png) I most likely (and as per-usual) left out something critical. | ||
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ComaDose
Canada10357 Posts
On August 18 2011 04:13 Aletheia27 wrote: It's a quantum physics problem actually.... but i don't want to answer this cause I don't havea good question You should answer and give a lame question then.... now I'm googling cause I feel ignorant. Its pretty much your calling to continue this thread. EDIT: Your proof is true but a little.... shallow, like i mean just missing some whys and therefore... pretty much exactly like a professional would do it good job ;p randall from xkcd helped me understand it better ;p linky EDIT: can your question be rewritten as this? + Show Spoiler + Suppose we have two entangled particles. Now we measure one of the particles to determine it's actual state. We know that instantaneously, the state of the other particle is set. However, it is impossible to determine any classical information from this instantaneous effect - i.e., cannot gain any physical information. Why? Or rather, what information do you think you could gain that you didn't have before? i.e. is the answer your looking for true for all entangled particles? | ||
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EsX_Raptor
United States2802 Posts
From now on, I will try a mathematical approach to every puzzle I encounter to save myself the potential time-loss of trying one with no solution. ;p ![[image loading]](http://i56.tinypic.com/2ccxcfc.png) M.C. Escher And someone still needs to answer ComaDose's question! On August 18 2011 04:06 ComaDose wrote: I propose a new question: "whoes 410th birthday is it and what is he famous for?" | ||
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EtherealDeath
United States8366 Posts
You know that if one measures Particle A to be in state 1, then B is in 0. If A is measured to be in state 2, then B is in 1, and conversely if you measure B, then A is immediately set if it has not already been set by measurement. Some have thought this could be used for FTL (faster than light) communication, since the "information transfer" is instantaneous. However, this is not the case. In short, what does measuring your particle tell you that you didn't already know? | ||
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