Question 19
The number $2009^{2009^{2009}}$ is given, written in base 10. In one step we make the following operation: we delete the first and last digit, and we add their sum to the number which remained after deleting the first and last digit.
a) If after a finite number of steps there remains a two-digit number, is it possible that that number is a perfect square?
b) If after a finite number of steps there remains a one-digit number. Determine that number.
a) If after a finite number of steps there remains a two-digit number, is it possible that that number is a perfect square?
b) If after a finite number of steps there remains a one-digit number. Determine that number.