Finding the Sum of the Digits of Numbers
How many integers between and are such that the sum of their digits is ?
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1 solution
For a given value of n, list the number of integers with n digits whose sum is 2. For example, when n= 1, we have only the number 2. When n = 2, we have 11 and 20, so there are 2 numbers. For n = 4, we have 1001,1010,1100, and 2000, so there are 4. In this way, the pattern stays the same, and for n, we have n numbers whose sum of digits is 2. We cannot have 22 digit number for that would be >= 10^21. So the answer is the sum of n from n=1 to n=21, which is 21*22/2 = 231. Ed Gray