8.1. What is the sum of the digits of the number $A=10^{50}-10^{40}+10^{30}-10^{20}+10^{10}-1$?
# Answer: 270.

Solution. The number is the sum of three numbers: a number composed of 10 nines followed by 40 zeros, a number composed of 10 nines followed by 20 zeros, and finally, a number composed of 10 nines. All the nines fall on the zeros in the other addends, so there is no carry-over, and the answer is $90+90+90=270$.

Comment. Correct answer without justification - 2 points.