Intellectual quiz.

7th grade, math Olympiad: A failing student, Vasya, tore three sheets of paper from his notebook. Some of them (possibly all) were torn into three or five pieces. Some of the resulting pieces of paper were torn again into three or five pieces, and so on. Could Vasya, by doing this, obtain exactly 2002 pieces of paper? Answers "yes" and "no" are not accepted; describe the solution. And, at Fireball's request, a slightly more difficult problem, 8th grade, again math: Someone, when asked what his ticket number was, answered as follows: "If all 6 two-digit numbers that can be formed from the digits of the ticket number are added together, then half of the resulting sum will be exactly my ticket number." Determine the ticket number. P.S. If no one can solve it, or the solution is not 100% correct, I will post the solution offered by the authors of the problems.