1. There were 21 consecutive natural numbers written on the board. When one of the numbers was erased, the sum of the remaining numbers became 2017. Which number was erased?
Answer: 104.

Solution: Let the numbers on the board be N-10, N-9,..,N, ..., N+10. Their sum is $21 \mathrm{~N}$. When one of these numbers - x - was erased, the sum became 2017, $21 \mathrm{~N}-$ $x=2017$. Therefore, $x=21 N-2017$, since this is one of these numbers, we get $N-10 \leq 21 N-2017 \leq N+10$. Solving the inequalities $\frac{2007}{20} \leq N \leq \frac{2027}{20}$, we get $N$ $=101$, therefore, $x=21 * 101-2017=104$.