3. The symbol $n$! denotes the product of positive integers from 1 to $n$, for example: $4 !=1 \cdot 2 \cdot 3 \cdot 4$. Consider the number $H=1 !+2 !+3 !+4 !+\ldots+2016 !+2017$! (a sum with 2017 terms). What is the tens digit of $H$?
(B) 7
(C) 1
(D) 3
(E) 6
(3) The correct answer is $(C)$.

The number 10! is a multiple of 100, as is every $n!$ for $n>10$. The tens digit of $H$ is then obtained by summing the first nine terms $1! + 2! + 3! + 4! + 5! + 6! + 7! + 8! + 9!$. We have:

$$
1 + 2 + 6 + 24 + 120 + 720 + 5040 + 40320 + 362880 = 409113
$$

and thus the tens digit of $H$ is 1.

Problem proposed by Carmelo Di Stefano.