2. The truant Vasya skipped one lesson every Monday in September of a certain year, two lessons every Tuesday, three lessons every Wednesday, four lessons every Thursday, and five lessons every Friday. Could it have turned out that he skipped exactly 64 lessons for the entire September? (All Saturdays and Sundays in September were weekends, and the other days were school days. September has 30 days.)
2. Suppose Vasya skipped exactly 64 lessons. Note that September contains four full weeks and two consecutive days. In one full week, Vasya skipped \(1+2+3+4+5=15\) lessons, i.e., in four weeks Vasya skipped exactly 60 lessons, and in the two consecutive days - 4 lessons. But if one of these two days is a weekend, then the remaining day is a Monday or a Friday, on which Vasya skips 1 or 5 lessons, and the total does not add up to 64, i.e., it does not fit. If both days are school days, then Vasya should skip an odd number of lessons (3, 5, 7, or 9), which also does not equal 64 when the total number of skipped lessons is calculated. Therefore, Vasya could not have skipped exactly 64 lessons.

Answer: could not.