Variation of Nim-Game?

Question

Let be 24 stones given. The two players A and B are allowed to remove either one or two stones. The player, who removes the last stone(s) is the winner.

The question: Can A win safely, if he begins ?

My thoughts:

It is possible, if A plays clever and B not. It is just important that B removes the 22nd stone or 23rd as A can removes one or two. So A has to force B to remove, at least the 22nd.

But "safely" means in each case, right ? And this would just be an example - could someone gives me a hint how to start, please ?

Thanks in advance

Answer 1

Yes, safely means that both players are playing optimally.
Start classifying numbers to winning and losing positions (a number $n$ corresponds to the game in which at the start there are $n$ stones).
$1,2$ are winning, thus $3$ is losing, thus $4,5$ are winning, thus $6$ is losing...

Answer 2

In fact, the beginner does not have a safe way to win here. Either way A moves, B can give back a situation where A has to play with the next lowest multiple of 3, and B can keep doing that till A has to play on 3, and so A can either take 1 or 2, and B gets to take whatever is left, and wins.