2. Thirty beads (blue and green) were laid out in a circle. For 26 beads, the neighboring one was blue, and for 20 beads, the neighboring one was green. How many blue beads were there?
Answer: 18 blue beads.

Solution. Let's find the number of beads that have both a blue and a green bead next to them: $26+20-30=$ 16. The number of beads that have only blue beads next to them is $26-16=10$. The number of blue beads is $\frac{10 \cdot 2+16}{2}=18$. Here is an example of such an arrangement. Let's denote a blue bead as (b) and a green bead as (g). Suppose the beads are arranged in a circle in the following order clockwise:

b g bbbb g b g g b g g bbbb g g g g b b g b b g g b b g g g,

where the first and last beads are adjacent. In this arrangement, all conditions are met, and there are 18 blue beads.

Comment. If the correct answer is given, obtained by trial and error, and a valid example of the arrangement is provided, but it is not shown that there cannot be other solutions - 4 points. Points should not be deducted for the lack of an example. For arithmetic errors, deduct $1-2$ points.