7-6. In an ornithological park, there are several species of birds, a total of 2021 individuals. The birds sat in a row, and it turned out that between any two birds of the same species, there was an even number of birds. What is the smallest number of bird species that could have been there?
Answer: 1011.

Solution. Estimation. We will prove that there could not have been three or more birds of the same species. Indeed, suppose birds of the same species $A, B$, and $C$ sit in that exact order. Let there be $2x$ birds between $A$ and $B$, and $2y$ birds between $B$ and $C$, then there are $2x + 2y + 1$ birds between $A$ and $C$, which is an odd number of birds, contradicting the condition. Since there are no more than 2 birds of each species, there must be at least 1011 species.

Example. We will provide an example where 1011 species could have been present. For instance, the birds could sit in pairs: two of the first species, two of the second species, and so on up to the 1010th species, with one more bird of the 1011th species at the end. There are many other examples.