Alice and Bob are playing a game. There are 'n' discs. Alice starts the game. The players play alternatively thereafter. In each turn, the players have to choose a number which is a power of 4, say 'd' and subtract it from 'n'. So 'n' will be 'n-d' now. A player who cannot choose a power of 4 to deduct in his turn will lose the game.

Example: if n = 4, then Alice will choose 4 and end the game for Bob. As he will be left with 0 in his turn and he cannot choose a power of 4.

What will be the optimal strategy for the players in this case? And in general how to find the optimal strategy for players? What are the rules of thumb?

We all love solving new problems :) But I have got this question, how do the problem setters make sure that they are creating a novel problem which did not appear on any judge before. Because If a person has solved a kind of problem before then he will likely to recognize that problem and hence there will be no fun in it.

So how do they check that their problem is unique?

I think googling will not help here as this is more of a "semantic thing" than mere "syntax" and hence there should be some other way?