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### 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

If the US Army wants the smartest people to fill out the ranks of the special forces, why restrict it to US citizens with army history?

When I was in the Army, I heard probably as many soldiers saying, “I thought about going SF, but…” as I have heard civilians say, “I thought about joining the military, but…” SF selection is very tough, and with good reason. Despite it’s known difficulty, they still have a lot of applicants. Recruiting from inside the Army is just a initial way of separating the wheat from the chaff. Even if they could eliminate every Call of Duty couch warrior just by reviewing their initial application, they would still be wasting a lot of resources. Recruiting from soldiers at least guarantees certain basic levels of physical fitness and military knowledge.

Will I need to fill out the ETIAS (new European Union visa regulation) every time I travel to a EU country? Are can I just fill it out ones and it's valid for life time?

The answer is somewhere inbetween.Each ETIAS will be valid for 3 years from the date of issue (or until the expiry date of the travel document).Full details can be found at: ETIAS - European Travel Information and Authorisation System

Is it necessary that we have to fill out the MDS form for the army after BDS?

Yes,To appear for interview for grant of short service commission in army dental corps, u got to qualify All India MDS entrance and secure a rank.Call letters for interview are sent based on your entrance exam rank.

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!