Question 2
The cards in a deck are numbered $1,3,\ldots,2n-1$. In the $k$-th step, $1\le k\le n$, $2k-1$ cards from the top of the deck are transferred to the bottom one at a time. We want the new card on top to be $2k-1$, which is then set aside. After $n$ steps, the whole deck should be set aside in increasing order. How should the deck be stacked for this to happen if (a) $n=10$; (b) $n=30$?