Question 30
Alberto and Barbara challenge each other to the following game: initially on a table there are some piles of tokens (the number of tokens can vary from pile to pile). In turn, starting from Alberto, one of the two players makes one and only one of the following moves:
- or removes a token from a pile of his choice and eliminates it from the game;
- or divides a pile into two smaller piles, each of at least one token (without adding or removing tokens from the table).
Whoever removes the last chip from the table wins. Determine, depending on the number of piles on the table at the beginning and how many tokens they contain, which of the two players has a winning strategy.
- or removes a token from a pile of his choice and eliminates it from the game;
- or divides a pile into two smaller piles, each of at least one token (without adding or removing tokens from the table).
Whoever removes the last chip from the table wins. Determine, depending on the number of piles on the table at the beginning and how many tokens they contain, which of the two players has a winning strategy.