2. Bojan, Pavel, and Daniel solved 100 problems, with each of them solving 60 problems. All problems are divided into exactly two groups: "easy" and "hard." An "easy" problem is one that all three solved, and a "hard" problem is one that only one student solved. How many "easy" and how many "hard" problems did they solve together?
Solution. Let there be $x$ easy problems. Then each of the students solved $60-x$ hard problems. So

$$
3(60-x)+x=100
$$

which means $180-3 x+x=100$. From here $x=40$, so

![](https://cdn.mathpix.com/cropped/2024_06_05_d711adc0e32ac955c451g-1.jpg?height=248&width=315&top_left_y=1174&top_left_x=1164)
there are 40 easy problems, and 60 hard ones.