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Can you add 5 odd numbers to get 30?
It is 7,9 + 9,1 + 1 + 3 + 9 = 30Wish you can find the 7,9 and 9,1 in the list of1,3,5,   7,9    ,11,13,151,3,5,7,      9,1    1,13,15
Mathematical Puzzles: What is + + = 30 using 1,3,5,7,9,11,13,15?
My question had been merged with another one and as a result, I have added the previous answer to the present one. Hopefully this provides a clearer explanation. Just using the numbers given there, it's not possible, because odd + odd = even, even + odd = odd. 30 is an even number, the answer of 3 odd numbers must be odd, it's a contradiction. If what people say is true, then the question is wrongly phrased its any number of operations within those three brackets must lead to 30. Then it becomes a lot easier. Such as 15 + 7 + (7 + 1). That would give 30. But it assumes something that the question does not state explicitly and cannot be done that way. I still stick to my first point, it can't be done within the realm of math and just using three numbers, if not, then the latter is a way to solve it.EDIT:   This question has come up many times, Any odd number can be expressed as the following, Let [math]n, m, p[/math] be an odd number, [math] n = 1 (mod[/math] [math]2), m = 1 (mod[/math] [math]2), p = 1 (mod[/math] [math]2)[/math][math]n+m+p = 1 + 1 + 1 (mod[/math] [math]2)[/math]Let's call [math]n+m+p[/math] as [math]x[/math][math]= x = 3 (mod[/math] [math]2)[/math]Numbers in modulo n can be added, I'll write a small proof for it below, [math]a = b (mod[/math] [math]n), c = d (mod[/math] [math]n)[/math][math]a+c = b+d (mod[/math] [math]n)[/math]We can rewrite [math]b[/math] and [math]d[/math] in the following way, [math]n | (b - a) = b-a = n*p[/math] (for some integer p) [math]b = a + np[/math][math]b = a + np, d = c + nq[/math][math]b + d = a + np + c + nq[/math][math]b+d = a + c + n(p + q)[/math]Now we have shown that our result is true, moving forward, [math]3 = 1 (mod[/math] [math]2)[/math][math]x = 1 (mod[/math] [math]2)[/math]Therefore the sum of three odd numbers can never be even. It will always be congruent to 1 in mod 2.(This was what I wrote for a merged answer).Modular arithmetic  - Link on modular arithmetic, the basic operations. Modular multiplicative inverse - The multiplicative inverse in modular operations.Congruence relationFermat's little theorem Modular exponentiation - As title suggests.Good luck!
How should I fill out the preferences for the 5 IISERs?
A2AI will tell you my preference orderPuneMohaliKolkataBhopalTrivTirupatiBehrampurHowever I wanted only Pune or Mohali.Later I also realized that I didn't want Pune due to personal reasons so I'm lucky I got Mohali!Also I went to IISER Kolkata last year for Vijyoshi Camp and I can say that I'm happy I didn't get Kolkata because it's really far from the city and that thing really matters for me.All the Best!
China often notes it has 5000 years of history. On what basis? Is this an internationally agreed claim and could the same be said of other places on Earth?
Because the Chinese identify more with their early history than other places do. For example, French students learn about "the Romans", not "the French nation in 50 BC". Already the naming shows that we consider them a people apart, a people that gave us interesting ideas for sure but not a natural part of our own nation states. For China, the history of "our people" really goes back thousands of years.One of the unifying bands is the written Chinese language. It has changed less than European languages have. Plus the Chinese language is littered with phrases and expressions that were coined hundreds of years before Christ was born. There is also more awareness. Every Chinese child can recite by heart and understand poems that are 1400 years old (try that with Shakespeare, and he's much more recent).The final reason is that Chinese politicians play it up as a matter of national pride. For example, when China was recently criticized in the foreign news, a Chinese leader said "Whilst monkeys cry incessantly from bank to bank, I have already sailed past a myriad of mountains". This is not just a put-down of the foreign criticism and a declaration that China is already much more advanced, it's also two lines from a Tang dynasty poem that every Chinese person knows (早发白帝城, "Early start from Baidi" by poet Li Bai) - a not-too-subtle hint that China had world class poetry while Europe was overrun by barbarians.I'm currently working on a new method for learning Chinese - check it out at LearnYu - Automagic Chinese Course. Your support would be appreciated.
At what point does the ATF consider an AR-15 lower receiver a long gun when filling out the form 4473?
The law and ATF are quite clear on how a fire arm type is to be recorded on the form 4473.Section B line 16, handgun, long gun, other.Section D question 27 type of fire arm.Question 16. Type of Firearm(s):Quoting from the instructions for Form 4473"Other" refers to frames, receivers and other firearms that are neither handguns nor long guns (rifles or shotguns), such as firearms having a pistol grip that expel a shotgun shell, or National Firearms Act (NFA) firearms, including silencers. If a frame or receiver can only be made into a long gun (rifle or shotgun), it is still a frame or receiver not a handgun or long gun. However, frames and receivers are still "firearms" by definition, and subject to the same GCA limitations as any other firearms. See Section 921(a)(3)(B). Section 922(b)(1) makes it unlawful for a licensee to sell any firearm other than a shotgun or rifle to any person under the age of 21. Since a frame or receiver for a firearm, to include one that can only be made into a long gun, is a "firearm other than a shotgun or rifle," it cannot be transferred to anyone under the age of 21, nor can these firearms be transferred to anyone who is not a resident of the State where the transfer is to take place. Also, note that multiple sales forms are not required for frames or receivers of any firearms, or pistol grip shotguns, since they are not "pistols or revolvers" under Section 923(g)(3)(A)(Question 27) Question 24-28. Firearm(s) Description:These blocks must be completed with the firearm(s) information. Firearms manufactured after 1968 by Federal firearms licensees should all be marked with a serial number. Should you acquire a firearm that is legally not marked with a serial number (i.e. pre-1968), you may answer question 26 with "NSN" (No Serial Number), "N/A" or "None." If more than four firearms are involved in a transaction, the information required by Section D, questions 24-28, must be provided for the additional firearms on a separate sheet of paper, which must be attached to this ATF Form 4473.Types of firearms include, but are not limited to: pistol, revolver, rifle, shotgun, receiver, frame and other firearms that are neither handguns nor long guns (rifles or shotguns), such as firearms having a pistol grip that expel a shotgun shell (pistol grip firearm) or NFA firearms (machinegun, silencer, short-barreled shotgun, short-barreled rifle, destructive device or "any other weapon").End quote.To enter false information on the form 4473 would be committing a Federal felony. Therefore a stripped receiver must be marked as a receiver. If it is a stripped receiver regardless of manufactures markings, it must be recorded as a “receiver” on the form 4473.To answer the question posted. The ATF would consider an AR 15 receiver a long gun when the receiver is assembled as a long gun when it is transferred. Again a receiver only, is to be recorded as a receiver.
Is it necessary to fill out Form 15G/Form 15H if my service is less than 5 years? I need to withdraw the amount.
Purposes for which Form 15G or Form 15H can be submitted. While these forms can be submitted to banks to make sure TDS is not deducted on interest, there a few other places too where you can submit them. TDS on EPF withdrawal • TDS is deducted on EPF balances if withdrawn before 5 years of continuous service.
What are the best ways to reduce and eliminate belly, abdominal, and thigh fat?
Well, there are only 3 things that scare me in this world -- snakes, Port-o-Potties, and BELLY FAT.  So we need to get this situation under control or I'm going to freak right out man.  Its everywhere and its making me anxious and paranoid.  Just kidding around...Lets address the most common cause for people out there, and its the simplest one to start with -- they are overweight, period.  They eat too much junk, in way too big of portions, and don't exercise enough. Books have been written with vastly different and often contradictory approaches on how to solve this problem.In 10 years in the game, I can tell you this with absolute certainty -- there is no one, universal "right" way for everyone, everywhere.  Body type, activity levels, individual metabolic rate, hormonal variances, etc., all need to be taken into consideration.  Anyone who tells you differently is trying to sell you something or is propagating the tenets of a system that worked for them specifically, but may not work for every demographic across the board.  There are no simple answers to complex physiological processes, and cookie-cutting only works in the cookie making business.  Because trust me, in the real world beyond research and theory, I've seen various "plans" yield outstanding results.In general, if you are sedentary (and have no plans of putting on some spandex and pumping iron), then I feel the best approach is probably a Paleo-style diet.  In addition, make an effort to add some non-exercise specific calorie burning, such as a daily walk.  In other words -- eat like a caveman, live like a caveman (walking around everywhere, eating wild animals, vegetables, and seasonal fruits), look like a caveman -- healthy and fit, but not in peak physical condition or ripped, etc.If you are planning on some intense training to get the job done, well that changes the ball game entirely.  Exercise, specifically strength training, changes your internal physiology for up to 48-72 hours after the session (assuming you are lifting more intensely than Richard Simmons).  And anaerobic training runs via a different energy production pathway than low intensity daily/sedentary activity.  This changes the fuel dynamics of the body, along with recovery and tissue repair requirements, which means it changes nutritional needs.  For this demographic, I believe in strength training to boost the basal metabolic rate, walking to increase non-exercise specific calorie burning without some of the negative drawbacks of traditional cardio (namely joint and hormonal stress), and a moderate carb (lower fat/fat as by-product of protein sources) diet to fuel and recover from anaerobic training.  In other words -- train like a fitness athlete, live like a fitness athlete (staring at yourself in the mirror all of the time but pretending you are doing something else), look like a fitness athlete -- healthy, fit, and ripped.If you are looking for more specifics, I've written several answers on the Q that encompass this philosophy and give more detailed advice based on body type, activity levels, and physique goals.Now, onto more specifics -- foods or lifestyle choices that lead to fat accumulation specifically around the midsection:1.  Two of the most abundant compounds in the average, modern American diet are two of the worst compounds for body composition enhancement AND overall health -- concentrated fructose and trans-fats.  Both of these compounds have been researched and proven to be linked to many of our most troublesome diseases, and for this question's purposes, have been linked directly to resistance and abdominal obesity. For you science "geeks" (myself included), here are some links to a few research abstracts:http://www.ajcn.org/content/76/5...http://www.ncbi.nlm.nih.gov/pubm...In practical terms, "you gotta cut the crap".  Try to reduce trans fats (coming mostly  from packaged/refined snack foods, anything with hydrogenated oil, margarine, fried foods, etc.).  Also cut out concentrated sources of fructose:  high fructose corn syrup, sugar (which is technically one molecule of glucose plus one molecule of fructose), fruit juice and dried fruits, and B.S. foods that are marketed as "health" foods and better than sugar but contain just as much, if not more fructose, than table sugar (ie agave nectar, honey, etc.).  Fructose should be consumed in much smaller amounts than in the average American diet, and in the way in which mother nature intended -- via seasonal whole fruit.If you stick to this first principle alone, that should take care of about 90% of the problem.  Almost everything else related to belly fat accumulation can be related to the hormone cortisol.  And while a necessary and integral part of normal functioning, problems (including that damn belly fat) can arise with chronic overproduction.2. Stress.  Modern living and corporate/business/financial pressure have us all way more wound up than we should be.  But dude, I'm not one of these whacked out trainers that's gonna tell you to quit your job and come contemplate the meaning of life with me in the mountains.  You just have to try as much as you can to find ways to reduce stress a little bit -- intense strength training is a physical stress, but also can be an emotional release, and has a calming effect on the body upon completion, I'm too ADD and perverted to meditate (maybe it will work for you) -- but my answer to that seems to be walking (ie take a walk to calm your mind when work or life is freaking you out), deep breathing, yoga, stretching, hitting a punching bag, squashing bugs, whatever works for you man, I don't care.  Its an individual thing.  Oh, and I almost forgot the most important stress reliever of all time -- get some action, get some "loving".  Do I have to spell it out for you? Get laid already.  If you can't find someone, I'll help you out, my number is...just kidding, I already have my Queen.3.  Stress response to foods.  There are many of us that have allergies, or at least are sensitive, to specific food compounds.  Some specific ones that come to mind are gluten (the protein in wheat, rye, barley) and lactose (the sugar in milk).  If you have a full-blown allergy, you'll know it -- digestive distress (you might have to run and face my #2 fear in the world -- Port-o-Potties).  But many of us have a sensitivity that goes undiagnosed, and can lead to lethargy, water retention, and of course cortisol elevation and fat accumulation.  If you suspect this, try cutting out things like gluten and lactose for a few weeks and see how your body responds.4. Besides storing excess calories, one of the physiological purposes for excess body fat is to serve as a storage site for toxins.  Take in a lot of toxins through the environment or through foods, and you have an additional reason to store belly fat.  How can you reduce toxin exposure?  You can buy organic produce (regular produce is often sprayed with pesticides that act as toxins in our body).  You can cut back on alcohol, which the body treats as a toxin.  You can reduce your consumption of packaged foods -- I can't help but think that all of those chemicals, preservatives, and artificial sweeteners are somewhat perceived as toxins in the body.  And finally, eat more detoxifying foods (and not some B.S. detox plan designed to sell you 100 different supplements).  I just mean real foods that naturally serve as detoxifiers -- ie organic vegetables.5.  I am a coffee addict, but the research is quite clear that caffeine can elevate cortisol levels.  Moderate amounts should not have any detrimental effects on body composition (and can actually assist in the fat loss process by increasing lipolysis and acting as a thermogenic aid), but if you are eating like crap, not getting quality energy from real food, and just using caffeine and fake energy to compensate (ie drinking a pot of coffee a day, plus 20 red bulls, and 50 diet soda's), we'll you can see where that might lead to problems.  And if you are just using coffee as a vessel for sugar and cream, you don't really like coffee that much (you like sugar and cream).6.  Now I know some of you are thinking, this dude's crazy.  I'm not cutting out all of that.  I have to live my life.  I get it.  But my philosophy has always been to present the absolute ideal scenario, just so I don't undereanyone's ability or desire to "take things 100% all the way".  In reality, its up to you to find your own compromises.  What has worked well for most of my private clients is to get them to follow the 85% rule.  Follow the ideal path 85% of the time, and 15% of the time do whatever you want.  If you do that, you will do just fine.  Imagine what cutting out all sugar 85% of the time could do for your body and health?   7. The Fit Everywhere Else But Fat On the Belly -- Syndrome.  This is a technical one geared towards hard training athletes, so if you are neither, you might want to skip this one.I'm seeing this syndrome more and more in the gyms these days, as super low carb diets designed for the sick, sedentary population are being adopted by fit athletes engaging in intense anaerobic training.  Remember what I said about different diets being more appropriate for different demographics?  The athlete's training creates a unique physiological and metabolic environment much different than the sedentary slug's.Here is the thing.  Strength training is a unique stress on the body, it creates huge cellular damage and resulting repair demands, along with depleting muscle glycstores.  Caveman, and modern sedentary office workers, were/are not inflicting the type of serious muscular micro-trauma induced by an hour of lifting weights.  A severe catabolic environment such as that should be offset by an anabolic environment facilitated by proper nutritional intake (which ultimately will lead to an adaptive response -- muscle gain, metabolic boost, fat loss, etc.).  This is not happening in today's Carbophobe Era.  And with no carbs in response to training, the body remains in a constant catabolic state where cortisol is the dominant hormone. You get no muscle growth, the breaking down of lean muscle tissue as a fuel, and cortisol elevation leading to fat accumulation around the midsection -- guys and gals who are consistently training hard, following the low-carb trend, "thinking" they are doing everything right, are pretty lean everywhere else, but have that nice layer of flab hanging over their belt line.If you think I'm full of crap, here is a link to a study that looked at carb intake and the free testosterone:cortisol ratio in response to anaerobic training (one of the few studies that uses athletes to draw conclusions rather than sedentary people):http://www.ncbi.nlm.nih.gov/pubm...Insulin is a misunderstood hormone these days in the low-carb Era.  No hormone your body produces naturally is inherently bad, it just needs to be controlled.  Chronic elevation or overproduction can of course lead to fat gain.  But in the right amounts and situations (ie following an intense workout where sensitivity is high) it can be a good thing (anabolic, anti-catabolic, leading to increased lean muscle, elevated metabolic rate, which in turn leads to more fat burning at rest).If this resonates with you, my best advice is (I know it sounds crazy, but reread above) -- add some non-fructose, non-gluten containing carbs back into your diet (ie potatoes, sweet potatoes, rice) to REDUCE belly fat.  At the very least, start with a small amount in the post-workout window (0-45 min post training).  Keep your protein:carb ratio around 1:1 (if you have 30g of protein go with 30g starchy carbs).Alrighty then, that's enough for now.  It's 80 degrees in San Francisco.  Time to go fulfill my secret duties as a super hero and fight some belly fat.
How easy or hard is it to find a cab from anywhere in SF to another point in SF?
It can be iffy to find a cab from the Quora event at Terra in the SOMA neighborhood in the evening. But it is an easy enough walk to Market street where cabs are plentiful. You'd likely find one before you even get to Market street.As for the broader aspect of your question, it is difficult to answer. Some neighborhoods have excellent 24-hour cab availability, some have virtually no cabs to speak of unless you call for one (415-333-3333). If you want to know about a specific area, I can give my best estimate. Honestly, most people have no reason to visit the majority of this 47 square mile city, and the areas most people are likely to find themselves are the same areas that have decent to good cab service.
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