7.3. There are three automatic coin exchange machines. Among them, the first machine can only exchange 1 coin for 2 other coins; the second machine can only exchange 1 coin for 4 other coins; the third machine can exchange 1 coin for 10 other coins. A person made a total of 12 exchanges, turning 1 coin into 81 coins. Try to determine: how many times did he use the first and second coin exchange machines, respectively?
7.3. The first coin exchanger increases the number of coins by 1 each time, the second coin exchanger increases the number of coins by 3 each time, and the third coin exchanger increases the number of coins by 9 each time. Let the three coin exchangers be used $A$ times, $B$ times, and $C$ times, respectively, then we have
$$
A+B+C=12, A+3 B+9 C=80 \text {. }
$$

By exhaustive search and examining the remainders when divided by 3 and 9, we can find that $A=B=2, C=8$.