At the central telegraph office, there are change machines that exchange 20 kopecks for 15, 2, 2, and $1 ; 15$ kopecks for 10, 2, 2, and $1 ; 10$ kopecks for 3, 3, 2, and 2. Petya exchanged 1 ruble 25 kopecks in silver for copper. Vasya, looking at the result, said: "I know exactly what coins you have" and named them. Name them as well.
Since two 15-kopeck coins can be exchanged for the same combination as a set of one 10-kopeck and one 20-kopeck coin, Petya could not have had more than one 15-kopeck coin in his original set, nor could he have had both a 10-kopeck and a 20-kopeck coin simultaneously.

It is impossible to get 125 kopecks using only 10 and 20 kopeck coins, so Petya must have had a 15-kopeck coin. The remaining coins, totaling 110 kopecks, must have been identical, hence they were 10-kopeck coins.

With such a set of coins, the result of the exchange can indeed uniquely determine the original coins: Petya ended up with just one kopeck; from this, it can be concluded that he did not have any 20-kopeck coins initially, and had only one 15-kopeck coin.

## Answer

One 15-kopeck coin and 11 ten-kopeck coins.