Counting and counting...
Number Theory
Level
4
How many integers from to inclusive have their sum of digits (in base 10) divisible by 5?
The answer is 199999.
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1 solution
It is easy to observe that for every 10 number, there exists an integer of which sum equals 5 n . Adding a 5 to it produces a number whose sum equals 5 n + 5 whichnis also included in the same set of number. Therefore, answer is 1 0 0 0 0 0 0 / 1 0 ∗ 2 − 1 , the one is being deducted, just because there don't exist two such number in the first ten integer.