10.1. What is the sum of the digits of the number $A=100^{40}-100^{30}+100^{20}-100^{10}+1$?
# Answer: 361.

Solution. The number is the sum of three numbers: a number composed of 20 nines followed by 60 zeros, a number composed of 20 nines followed by 20 zeros, and finally the number 1. All nines and the one fall on the zeros of the other addends, so there is no carry-over, and the answer is $180+180+1=361$.

Comment. Correct answer without justification -2 points.