8.3. There are 19 cards. Can a non-zero digit be written on each card so that these 19 cards can be arranged to form a 19-digit number divisible by 11?
8.3. Answer: Yes.

Write a 2 on each of 10 cards, and a 1 on each of the remaining cards. It is well known that a positive decimal integer is divisible by 11 if and only if the difference $S$ between the sum of the digits in the odd positions and the sum of the digits in the even positions is a multiple of 11. Under all different arrangements of the 19 cards, we have
$$
-7 \leqslant S \leqslant 11,
$$

where only 11 is a multiple of 11, corresponding to placing the cards with 2s in all odd positions and the cards with 1s in all even positions.