2. Two players take turns to write natural numbers on a board. The rules forbid writing numbers greater than $\mathrm{p}$ and also divisors of previously written numbers. The player who has no move loses.
Determine which player has a winning strategy for $\mathrm{p}=10$ and describe this strategy.
Soln.
The first person wins $\quad[1 \mathrm{mk}]$
by playing $6 . \quad[1 \mathrm{mk}]$
After that the only plays are $4,5,7,8,9,10$.
We group these numbers in pairs $(4,5),(7,9)$ and $(8,10) . \quad$ [1 mk]
It is clear that these give a reply to the subsequent plays of the second player.