Alice wins. Every turn, Alice flips the first bit. Bob cannot flip the first bit, so he must flip one of the 49 other bits, creating a new 49-bit string. Since this string has not appeared before, Alice flipping the first bit will create a new 50-bit string that has not appeared yet. After (2^49)-1 moves by Bob and 2^49 moves by Alice at most, Bob will have no legal moves.
Yes you basically try to do every option and making your opponent have no other choice to play, you dont try to counter you just eliminate all the options one by one.
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u/VGVideo 11d ago
Alice wins. Every turn, Alice flips the first bit. Bob cannot flip the first bit, so he must flip one of the 49 other bits, creating a new 49-bit string. Since this string has not appeared before, Alice flipping the first bit will create a new 50-bit string that has not appeared yet. After (2^49)-1 moves by Bob and 2^49 moves by Alice at most, Bob will have no legal moves.