1. In a row, the numbers $1,2,3, \ldots, 2014,2015$ are written. We will call a number from this row good if, after its removal, the sum of all the remaining 2014 numbers is divisible by 2016. Find all the good numbers.
Answer: The only good number is 1008.

Solution. The remainder of the division of the sum of all 2015 numbers by 2016 is 1008:

$(1+2015)+(2+2014)+\ldots+(1007+1009)+1008=2016 \cdot 1007+1008$.

Therefore, only 1008 can be crossed out.

Scoring. 12 points for a correct solution. If it is shown that 1008 is a good number, but it is not proven that there are no other good numbers, 6 points.