7.1. Six consecutive numbers were written on the board. When one of them was erased and the remaining ones were added up, the result was 10085. Which number could have been erased? List all possible options.
Answer: 2020 or 2014

Solution. Note that the sum of five consecutive numbers is equal to the middle number multiplied by 5. If we have five out of six consecutive numbers, and they are not consecutive, then we can increase 1, 2, 3, or 4 of them by 1 so that the numbers become consecutive. Since the sum of the given numbers is divisible by 5, they were consecutive, otherwise, we increased no more than 4 of them, and the sum became divisible by 5 again.

Thus, we have 5 consecutive numbers, and the middle one is 10085: $5=2017$. But then our remaining numbers are 2015, 2016, 2017, 2018, 2019, so the number that was crossed out is 2014 or 2020.