MathDB

The numbers

1, 19, 199, 1999,\ldots

are written on several cards, one card for each number.
[*]Is it possible to choose at least three cards so that the sum of the numbers on the chosen cards equals a number in which all digits, except for a single digit, are twos? [*]Suppose you have chosen several cards so that the sum of the numbers on the chosen cards equals a number, all of whose digits are twos, except for a single digit. What can this single different digit be?

Problem Statement