This puzzle is a follow-up of Coins on a table (warning: the link contains the answer to the original question).
You are playing a game against your friend Alice:
- first Alice places one coin on a rectangular table (she can choose where to put it).
- Then it's your turn: you choose where to place the second coin on the table.
- Then Alice places another coin.
- Then you place another coin.
- and so on, until there is no space left to place any other coins. The player who cannot place its coin loses.
You have an unlimited supply of identical coins -although you can use them only for this game, I'm sorry. The coins cannot overlap nor lie outside the boundary of the table.
If Alice plays first, who has a strategy to win this game? (this was the original question)
Original part of the puzzle:
It is well known that Alice is a bit distracted. Even if she has a strategy to win this game (i.e. even if she can choose whether to go first or second depending on the answer of the previous question) she always get her first move wrong. That means that she does not play the move that allows her to win: she plays another move of their choice. Then she realizes her mistake and she plays correctly for the rest of the match.
In this scenario can you always win this game?
In other words: do you always have a strategy after Alice's first move or does it depend on "how wrong" is Alice's first move?