1.1. If you add the last digit of a number to the number itself, you get 5574, and if you add the second-to-last digit, you get 557. What is this number?
Answer: 5567

Solution. Note that the guessed number differs from 5574 by one digit, so the guessed number is not less than $5574-9=5565$ and not more than 5574. Then the second to last digit of the number is 6 or 7, so our number is 5566 or 5567. The first one does not fit, but the second one does.