Question 2
A positive integer $N_0$ is written on a board. Players A and B alternate, A starting, replacing the current positive integer $N$ by either $N-1$ or $\lfloor N/3\rfloor$. The first player to write 0 wins. Determine which player has a guaranteed winning strategy when (1) $N_0=120$; (2) $N_0=(3^{2002}-1)/2$; (3) $N_0=(3^{2002}+1)/2$. Here $\lfloor x\rfloor$ is the greatest integer not exceeding $x$.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; this rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.
The supplied PDF does not state a time limit. This edition uses the user-approved 240 minutes per session, 480 minutes total for both sessions; this is an editorial convention. The supplied source has no question point values. Each problem uses 1 editorial point for import compatibility; this is not an official scoring scale. Essay grading is manual; this rubric is editorial. Import multipliers: correct 1, incorrect 0, blank 0.