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You are not logged in. #1 20121218 04:42:40
Sum of 3 digits and its compliment to 1000Can you notice any patterns in the sums of the digits in three digits numbers and the sums of the digits of their complements to 1000. #2 20121218 06:08:19
Re: Sum of 3 digits and its compliment to 1000For now I only have 10 and 28... The limit operator is just an excuse for doing something you know you can't. “It's the subject that nobody knows anything about that we can all talk about!” ― Richard Feynman “Taking a new step, uttering a new word, is what people fear most.” ― Fyodor Dostoyevsky, Crime and Punishment #3 20121218 08:28:22
Re: Sum of 3 digits and its compliment to 1000Let be a threedigit number. Then . If , we write . Then the sum of digits is . If , we have . If , the sum of digits is . If , then and the sum of digits is . So the sums are (i) 28 if (ii) 19 if and (iii) 10 if and #4 20121218 16:23:49
Re: Sum of 3 digits and its compliment to 1000If you cast out nines on the sum of the digits of both numbers together, the cast out digit will be 1. Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. #5 20121218 19:39:16
Re: Sum of 3 digits and its compliment to 10001000333=667 246 pages on Prime Numbers Wiki (+1) #6 20121218 21:08:18
Re: Sum of 3 digits and its compliment to 1000Wow first time using this forum so I didn't expect an answer as thorough as scientia's. I wish I had more bonus points to give out. #7 20121218 21:10:14
Re: Sum of 3 digits and its compliment to 1000In general, if you have an ndigit number and is the n or (n−1)digit number that when added to makes , then: If is the smallest integer such that , , then , , and , . Thus the sum of digits is . Example: This is equal to (8 is the no. of digits of N and 4 is the lowestplaced nonzero digit of N). Last edited by scientia (20121218 21:10:50) #8 20121219 02:57:01
Re: Sum of 3 digits and its compliment to 1000And if casting out nines on the sum of the two complementary numbers, the result will still always Writing "pretty" math (two dimensional) is easier to read and grasp than LaTex (one dimensional). LaTex is like painting on many strips of paper and then stacking them to see what picture they make. 