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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!
_+_+_+_+_ = 30. How do you fill in the blanks using 1, 3, 5, 7, 9, 11 or 13?15 + 13 + (11-9) + (7-5) + (1-3) = 30
Why don't schools teach children about taxes and bills and things that they will definitely need to know as adults to get by in life?Departments of education and school districts always have to make decisions about what to include in their curriculum. There are a lot of life skills that people need that aren't taught in school. The question is should those skills be taught in schools?I teach high school, so I'll talk about that. The typical high school curriculum is supposed to give students a broad-based education that prepares them to be citizens in a democracy and to be able to think critically. For a democracy to work, we need educated, discerning citizens with the ability to make good decisions based on evidence and objective thought. In theory, people who are well informed about history, culture, science, mathematics, etc., and are capable of critical, unbiased thinking, will have the tools to participate in a democracy and make good decisions for themselves and for society at large. In addition to that, they should be learning how to be learners, how to do effective, basic research, and collaborate with other people. If that happens, figuring out how to do procedural tasks in real life should not provide much of a challenge. We can't possibly teach every necessary life skill people need, but we can help students become better at knowing how to acquire the skills they need. Should we teach them how to change a tire when they can easily consult a book or search the internet to find step by step instructions for that? Should we teach them how to balance a check book or teach them how to think mathematically and make sense of problems so that the simple task of balancing a check book (which requires simple arithmetic and the ability to enter numbers and words in columns and rows in obvious ways) is easy for them to figure out. If we teach them to be good at critical thinking and have some problem solving skills they will be able to apply those overarching skills to all sorts of every day tasks that shouldn't be difficult for someone with decent cognitive ability to figure out. It's analogous to asking why a culinary school didn't teach its students the steps and ingredients to a specific recipe. The school taught them about more general food preparation and food science skills so that they can figure out how to make a lot of specific recipes without much trouble. They're also able to create their own recipes.So, do we want citizens with very specific skill sets that they need to get through day to day life or do we want citizens with critical thinking, problem solving, and other overarching cognitive skills that will allow them to easily acquire ANY simple, procedural skill they may come to need at any point in their lives?