Problem 7.6. A row of 101 trees has been planted: poplars, birches, and pines. Between any two poplars, there is at least one tree, between any two birches, there are at least two trees, and between any two pines, there are at least three trees. How many pines could have been planted? List all possible options.
Answer: $25,26$.

Solution. Consider any four consecutive trees. If there is no pine among them, then the trees there alternate (two identical trees cannot stand next to each other) between birch and poplar, but then there would be only one tree between two birches, which is impossible by the condition. Therefore, among any four consecutive trees, there must be a pine.

It is also clear that among any four consecutive trees, there cannot be two pines, otherwise there would be fewer than three trees between them.

Let's divide the entire row of trees into 25 quartets and one tree. In each quartet, there is exactly one pine, so there are 25 or 26 pines in total (depending on which tree is left over).

Both cases are possible, as can be seen from the following examples (periods are underlined):

$$
\begin{aligned}
& \frac{\text { P, B, P, T }}{\text{T}}, \underline{\text{P}, \text{ B, P, T}}, \ldots, \text{P}, \text{ B, P, T}, \text{ P } \\
& \underline{\text{T}, \text{ P, B, P}}, \text{T}, \text{ P, B, P}, \ldots, \text{T}, \text{ P, B, P, T. }
\end{aligned}
$$

Remark. It can be proven that no other examples, except for those given above, exist.