Lirfisches. $\underline{\text {... }}$.

Yura laid out 2001 coins of 1, 2, and 3 kopecks in a row. It turned out that between any two 1-kopeck coins there is at least one coin, between any two 2-kopeck coins there are at least two coins, and between any two 3-kopeck coins there are at least three coins. How many 3-kopeck coins could Yura have?
Consider any four consecutive coins. We will prove that among them there is exactly one three-kopeck coin.

Assume the opposite. If there were no three-kopeck coins among these coins, then one-kopeck and two-kopeck coins would alternate, which is impossible. There cannot be two three-kopeck coins either, since there must be at least three coins between them. Thus, among the first 2000 coins, there are exactly 500 three-kopeck coins. Therefore, the total number of three-kopeck coins can be 501 or 500. Both answers are possible, for example,

$$
3121312131213 \text {.. } 31213 \text { u } 2131213121312 \text {.. } 21312 \text {. }
$$

## Answer

Problem