7. There is a stack of 200 cards, numbered from 1 to 200 from top to bottom. Starting from the top card, perform the following operations in sequence: remove the top card, and place the next card at the bottom of the stack; then remove the top card (originally the third card), and place the next card at the bottom of the stack... Repeat this process. What is the number of the card that remains?

The card that remains is the original card number $\mathbf{2 0 0}$ out of the 200 cards.
【Analysis】For the circular cat and mouse problem, the power of 2 closest to 200 is 2 to the 7th power - 128, $200-128=72$, so the 72nd card taken away is the 143rd card. At this point, there are 128 cards left. Now, the operation continues, the first card is the 145th card, and the remaining one is the last card at this point, which is the 144th card. Thus, the remaining card is the 144th card.