question archive Write a 4 pages paper on magic number 1089
Write a 4 pages paper on magic number 1089
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Write a 4 pages paper on magic number 1089. The procedure that yields the number 1089 through calculations bearing three digit numbers involves three basic steps. The first step involves a random selection of a three-digit number, which has the first and last digits having a difference of more than two. Secondly, the digits are reversed, this changes the order of the numbers such that the first one appears as the last and the last as the first. For example, 469 is reversed to become 964. After this, the smaller of the numbers is subtracted from the one that has a bigger value. From the example above it will be (964-469)= 495. Finally, the number obtained in step two is added to its reverse hence generating the number 1089. In our example, 495+593 yields 1089. This procedure yields this number (1089) only given that the three digit numbers used always have a difference of more than two between the first and the last numbers.
To unravel the mystery behind the magic behind the mathematical logic we can systematically analyze the calculations. If the three digits in our number are a, b and c respectively. then, we establish the three digit number will be given by (100*a) + (10*b) + c. this means that when the number is reversed, it becomes. (100*c) + (10*b) + a. Engaging the next step in the calculation which involves a subtraction of the biggest number from the smallest (in this case we can use any of the numbers since we are not certain which letters represents the largest number). (100a+10b+c) – (100c + 10b + a) yields 99 (a-c). The logic here is that (a-c) must always be greater than two and definitely not greater than 9. The trick is usually in the predictable numbers that are obtained after the process gets to this level. It is a must that the values of 99 (a-c) should be either 198, 297, 396,495, 594, 693, 792, or 891.
