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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!
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
What would cause my 13-year-old daughter’s mouth to just completely fill up with blood then shortly after come out her nose?
Possibly a nose bleed - but this is not a forum to replace medical care, get her to the ER ASAP it could be serious. This happened to me at age 12 at summer camp, during my sleep and my mouth filled with blood, all over my pillow, and my nose bled, and it was determined by the local hick doctor that he couldn’t figure it out. I had a ruptured blood vessel in my nose when I sneezed in my sleep - specialists said months later. That next year I had rheumatic fever which changed the course of my life putting me on steroids, antibiotics, and a half year of bedrest, with no exercise for several years. GET HER TO AN ER
My 13 year old took nails and nailed the curtains into the wall with out a rod or anything. 8 nails total. How do I correct this behavior?
Sounds like you have a future carpenter‡ To correct the behaviour, starts with yours! It is obviously not the kids fault for your stupidity! I have to ask “why” there weren’t curtains to protect the privacy of your child in the first place. Don’t come down on your kid for your bad behaviour. YOU are supposed to be leading by example, I’m on the side of the kid! You are NOT a good example, and they are just trying to find their way through the mess of you! Correct your behaviour!Then teach the right way! Start by showing the right way without any anger!Involve them in the whole process. Show how to get the right materials, show how to remove the nails without doing further damage. Then show how to fix the damage, then painting etc. Have them help, even do! Then show how to install the rods and drapery in the correct manner.To be clear, this is your fault, not the child, show them how to do it right, then they will in the future!
Is it normal for a filling to come out after 8 years, while chewing gum?
Normal is a misnomer. Does it happen? Yes. Often? Maybe. Could I have done something to accelerate the loss of my filling? Probably.Fillings aren't for life, as much as we would want them to be. No matter how amazing our technique is, there are so many variables that at best you are looking at 10–15 years for a “white” filling (resin composite material). That's according to scientific literature.Things that affect how long a filling will last will be things out of your (the patient’s) control like - technique, saliva isolation, your tooth structure (if it is hypomineralised for example, the bond strength to the tooth won't be as good), the shape and size of the cavity.Things that are out of our control (the dentist) can be well within the patients control - things like oral hygiene, acid wear issues (how much you snack, eat/drink acidic things like coke or red wine or OJ, drink something before bed, brush right after eating…all these can play a part in creating a very acidic environment in your mouth for a filling that is relying on the bond strength (the glue) to hold it in place, it can sometimes get eaten away by the acid), grinding/clenching issues that are t being addressed, biting into something hard on a regular basis (or even just once but in the right spot) like nuts or pork crackling….So in answer to your question, yes it's normal to lose a filling chewing gum after 8 years. Be glad you got a good 8 years from it, hopefully it's easy to replace and hopefully you will avoid those things on the second list that you have an impact on, to extend the life of the next filling :)
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