Question 93
Amina has a deck of cards numbered from $1$ to $101$. Initially, she holds $50$ cards in her hand, while the remaining cards are laid face up on the table. In one move, she can swap all $50$ cards in her hand for any $50$ cards from the table. Amina wants to obtain all the cards numbered from $1$ to $50$ in her hand in at most $N$ moves. What is the minimum $N$ that guarantees she can always achieve this, regardless of her starting hand?