2018 again? #3
Number Theory
Level
pending
To a number I subtract the sum of its digits, and of the resulting number I extract a digit in such a way that the sum of the remaining digits of the resulting number is 2018. What digit have I extracted?
1
5
0
7
3
6
4
2
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1 solution
Let the number be n and let its sum of digits is denoted by S ( n ) , then we have that n − S ( n ) is divisible by 9 .
According to the question, if you extract one number from it, the sum of its digits is 2 0 1 8 , therefore we must have an integer 0 ≤ x ≤ 9 such that 2 0 1 8 + x is divisible by 9 .
We see that the only such number is 7 , since 2 0 2 5 is divisible by 9 .