17. Carolina starts writing all positive even integers, one after the other: 246810121416... Which digit will occupy the $2017^{th}$ position?
(A) 8
(B) 7
(C) 2
(D) 5
(E) 1
(17) The correct answer is $(E)$.

Caterina writes the 4 even single-digit numbers, for a total of 4 digits. Then she writes the 45 even two-digit numbers, those between 10 and 98, for a total of 90 digits. She then writes the 450 even three-digit numbers, those between 100 and 998, for a total of $3 \cdot 450=1350$ digits. At this point, she will have written $4+90+1350=1444$ digits, and there will be $2017-1444=573$ digits left to write.

The next numbers are four-digit numbers. Since $573=4 \cdot 143+1$, the digit in the $2017^{th}$ position will be the first digit of the one hundred forty-third even four-digit number. This number is 1286, and its first digit is 1.

Problem proposed by Carmelo Di Stefano.