Math Olympiad problem (Oct 4)

[Wyman]

[ QUOTE ]
Oh, and try now to solve the general problem, n counters and players remove between one and m

Same solution?

[/ QUOTE ]

No. Player one wins unless n is a multiple of M+1.

Strategy: At each turn, p1 removes stones to leave a multiple of M+1 for p2. Notice that mod M+1, p2 can never leave 0 stones, and p1 will win.

Of course, if p1 starts with 0 mod M+1 stones, he must leave a nonzero number mod M+1 for p2 after the first move. By the above, p2 will win.