2. Excellent student Vasya solves exactly 1 algebra problem and 11 geometry problems, or 3 algebra problems and 8 geometry problems, or 15 algebra problems and no geometry problems each day. Over a certain period, Vasya solved 100 algebra problems. Could he have solved 144 geometry problems during this time?
Answer: No.

Solution: Note that the number of geometry problems solved in one day differs from the number of algebra problems solved by a multiple of 5. Therefore, the total number of geometry problems solved should differ from the total number of algebra problems solved by a multiple of 5. However, $144-100=44$ is not divisible by 5.

Scoring criteria. Full solution - 20 points. Only for the correct answer or for considering special cases - 0 points.