B4. We have 10,000 cards numbered from 1 to 10,000. We always perform the following step: we remove all cards that have a square number and renumber the remaining cards consecutively starting from 1.

$\mathrm{After}$ how many steps do we have only one card left?
B4. 198

The first time we remove the cards numbered $1^{2}, 2^{2}, 3^{2}, \ldots, 100^{2}$. Then there are still 9900 cards left. Since $99^{2} \leqslant 9900<100^{2}$, in the second step we remove $1^{2}$, $2^{2}, \ldots, 99^{2}$. After that, there are $9900-99=9801=99^{2}$ cards left, exactly a square. In general, if we start with $n^{2}$ cards, where $n \geqslant 2$, we remove $n$ cards in the first step and $n^{2}-n$ cards remain. Since $(n-1)^{2}=n^{2}-2 n+1 \leqslant n^{2}-n<n^{2}$, we remove $n-1$ cards in the next step, leaving exactly $\left(n^{2}-n\right)-(n-1)=(n-1)^{2}$ cards. In two steps, we go from $n^{2}$ cards to $(n-1)^{2}$ cards. Therefore, we need $2 \cdot 99=198$ steps to go from $100^{2}$ cards to 1 card.