3. For two two-digit, positive integers $a$ and $b$, it is known that 1) one of them is 12 greater than the other; 2) in their decimal representation, one digit is the same; 3) the sum of the digits of one number is 3 greater than the sum of the digits of the other. Find these numbers.
Answer: $a=11 t+10, b=11 t-2, t=2,3, \ldots, 8$;

$$
\tilde{a}=11 s+1, \quad \tilde{b}=11 s+13, \quad s=1,2,3, \ldots, 6
$$