1. On the board, the number 1.11 is written ten times, and the number 1.01 is written eleven times. Can one or several numbers be erased so that the sum of the remaining numbers is equal to 20.19?
Solution. The sum of all the written numbers is $10 \cdot 1.11 + 11 \cdot 1.01 = 22.21$. This is 2.02 more than the required sum. Therefore, it is sufficient to erase two numbers 1.01. One can also verify directly that the sum of the numbers remaining after erasing is 20.19.

Answer: Yes, it is possible. The numbers to be erased are 1.01 and $1.01$.