Understanding the Problem
#999999 Color Conversion. The hexadecimal color #999999 has RGB values of R:153, G:153, B:153 and CMYK values of C:0, M:0, Y:0, K:0.4. Its decimal value is 10066329. ICD-9-CM 999.3 is one of thousands of ICD-9-CM codes used in healthcare. Although ICD-9-CM and CPT codes are largely numeric, they differ in that CPT codes describe medical procedures and services. Can't find a code? This hex color code is also a web safe color which is equal to #999. #999999 color name is Gray60 color. #999999 hex color red value is 153, green value is 153 and the blue value of its RGB is 153. Cylindrical-coordinate representations (also known as HSL) of color #999999 hue: 0.00, saturation: 0.00 and the lightness value of 999999 is 0.60. IconStiX是一款Mac上优秀的文件夹图标修改设计工具,可以快速的修改制定文件夹的图标,支持为文件夹图标上添加文字、图片、特效等,很不错! 2019年8月30日 3,194 发表评论.
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Iconstix 3 999 Digits
Recently in one of my classes we were presented with this problem: how many different ways can you get consecutive integers to add up to 9999? For example, can you do it with 2 consecutive integers? What about 3 consecutive integers? 4? 5? 6? The possibilities seemed endless. 2 and 3 worked, but 4 didn’t work. Is there some sort of pattern?
Our teacher then challenged us to see if we could figure out all the possibilities that would work. Through a lot of trial and error, using several different methods, our class eventually discovered that there were a total of 24 different numbers of consecutive integers that would add up to 9999.
We achieved these results using several different methods. Initially, I used the math-based search engine WolframAlpha to help me guess-and-check to see if certain numbers would work. For example, to see if there were 3 consecutive integers that added up to 9999, I entered n+(n+1)+(n+2)=9999 into the search bar. WolframAlpha told me that the solution was 3332. Since 3332 is an integer, that means that 3 is a viable solution to our question, and that the 3 integers are 3332, 3333, and 3334.
I continued to use this guess-and-check method until I had found about 12 different correct numbers of consecutive integers. I knew that the guess-and-check method wasn’t a viable method to find all possible numbers, so I looked at the solutions I had already discovered to see if I could discover a pattern. Our class discussed possible theories about how the solutions were related, and we eventually produced the theory that the solutions to this problem were all of the factors of 9999 along with their doubles. We once again used WolframAlpha to test this hypothesis, and discovered that this method did in fact produce all of the solutions.
We then changed our problem to see how many different sums of consecutive integers would produce 10,000. Surprisingly, this method didn’t work for 10,ooo. However, another one of our classmates discovered the following formula which did produce the correct results for both 9999 and 10000:
N = ½·n(2a+n-1)
N is be the desired sum, such as 9999 or 10000, n is the number of consecutive integers, and a is the initial term.
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Plugging this equation into WolframAlpha using whichever N you want to explore results in all of the possible solutions. This allows us to explore different values of N to see how many possible solutions there are for different numbers. We discovered that for all odd N values, the solution is the same as the 9999 solution: the possible n values are the factors of 9999 as well as their doubles. For even values of N, the solution is a bit more complicated — all of the odd factors of N as well as those factors times a power of 2. This can be seen in the image below, which shows the solutions for 10,000.
Technology’s Role
Technology was the basis for our class being able to understand and come to a conclusion about this problem. While it would be possible to test different numbers using pen and paper using the formulas that I plugged into WolframAlpha, it would be considerably more time-consuming and frustrating. Also, with the formula N = ½·n(2a+n-1) , WolframAlpha was able to automatically comb through all of the possible combinations of n and a and only select the integer solutions, whereas there is no easy way to do that same process by hand.
![Iconstix 3 999 Iconstix 3 999](https://www.blueberrybrands.com/retainedImages/Img001999_2.jpg)
As teachers, it will be important for us to keep in mind the opportunities that technology provides us. Traditionally, math students do everything by hand, with the exception of the occasional use of a handheld calculator, but they are rarely encouraged to use tools such as WolframAlpha in the classroom. However, tools such as this can be a key foundation to explorations such as the one I just described.
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Ah, sweet surrender.
September 9, 2016 breaks down to 9-9-9 (since “2016” = 2+0+1+6 = 9, making this a Universal 9 Year). The code is a message and also an energetic reality.
This day opens us to surrender on the highest realm. It is the end of a concerted struggle and a transition into wisdom or even a sense of rebirth.
Think about what has constituted your biggest or most consistent struggle—either in the past year, or even throughout your life. This is the time to put this issue (or issues) to center stage and into the spotlight. Now is the time to make some deep changes.
In Numerology, the number 9 is sacred and offers all of the lessons related to all the numbers 1-8. It challenges us to take the lead and embrace independence (1), to love and serve the needs of everyone (2), to express emotions in a healthy way and to be creative (3), to work hard and create stability (4), to use freedom constructively and have fun (5), to nurture and create a home (6), to live with a spiritual base and also ask questions (7), and to empower ourselves and to manifest in the material world (8).
The numerology of 999, day where there is a TRIPLE serving of 9 energy, it opens us—whether we “like” it or not—to our truth, in ways that we have been both searching for and avoiding. While we can say we want enlightenment, we often romanticize it, when the actuality is that enlightenment a painful process. It is a constant stripping away and revealing of Truth and also shines a light on how we must participate in creating what we want in the world.
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There is true beauty in the transition opening on this special day. And given we also have two eclipses in September—which themselves are known to accelerate change in a big way—the numerology of 999 in this particular year presents an opportune time to unveil your deepest desires and visualize what it would look and feel like to step into your new reality.
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TAKE THE LEAP. Have you been hovering around a decision for so long you can’t remember a time when it hasn’t been eating at you? For example, I know people who have been thinking about getting a divorce for years and just continue to hover in the relationship. A friend of mine said it so well: If you’re constantly thinking about whether or not you should be in your marriage, you shouldn’t be in your marriage! If you’re meant to be there, thinking about whether or not you should stay or go is simply not on the radar.
BE REAL about your actions and participation—while forgiving yourself fully and completely. Do you keep beating yourself up about something you did or didn’t do in the past? Do you replay it over and over again? I think it’s Byron Katie who observes that often we have one traumatic experience and yet our mind relives it so often, it is if we experience the trauma every time we replay it. This is the time to find a way to truly forgive yourself and move on. It’s up to you to find your way to do it—Therapy? Energy work? Hypnosis? A “Release” ritual? Whatever speaks to you, try it it.
EXPAND YOUR CONSCIOUSNESS. Oh, sure. Sounds so cliché. Yet the energy of the 9 is optimized when we can truly live the Buddhist tenant of being Present—when we can live in the moment, let go of the past without resentment, and be open and curious about the future. If there’s ever a time to clear our slate of negativity, this is it. And this is made more challenging by the current conditions we’re experiencing in the world. There is so much tumultuous change, it can be disconcerting. Yet if we can be the eye in the center of the hurricane—even in the most intense times—the rest of it will become so simple.