1. In the encrypted equation $А Б+A Б+A Б+A Б+A Б+A Б+A Б+A Б+A Б=A A Б$, the digits have been replaced by letters: the same digits are replaced by the same letter, and different digits by different letters. Find all possible decryptions. (I. Rubanov)
Answer. $25+\ldots+25=225$. Solution. Add AB to both sides of the given equality. We get the equality $10 \cdot A B=$ AAB+AB. Therefore, B+B ends in 0, that is, $B=0$ or $B=5$. If $B=0$, then $100 A=120 A$, from which $A=0$, which is impossible. If, however, B $=5$, then from the equation $100 A+50=120 A+10$ we find that $A=2$.