 Get

# sf-15 5 point preference

### FAQ

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? 