Three. (25 points) There are 288 sets of cards, totaling 2016 cards, each set consisting of $1,2, \cdots, 7$ and stacked in the order $1,2, \cdots, 7$ from top to bottom. Now, these 288 sets of cards are stacked together from top to bottom. First, discard the top five cards, then place the top card at the bottom, and continue discarding the top five cards, then placing the top card at the bottom, and so on, until only one card remains.
(1) In the above process, when only 301 cards are left, how many cards have been discarded?
(2) What is the last remaining card, and which set does it belong to?
(1) For the first 42 cards (in 6 groups each), according to the operation rule, after discarding 5 cards, the cards placed at the bottom are $6,5, \cdots, 1,7$. Thus, each number discards 5 cards.

And $288 \div 6=48, 48 \times 5 \times 7=1680$ (cards), $48 \times 5=240$ (cards), $2016-1680=336$ (cards). That is, when 1680 cards are discarded, each number has discarded 240 cards, leaving 336 cards. The arrangement of these 336 cards is
$$
6,5, \cdots, 1,7,6, \cdots, 1,7,6, \cdots, 1,7,
$$

When 35 more cards are discarded, the number 7 discards 4 more cards, so the card 7 has discarded a total of 244 cards.
(2) Note that if there are only $6^{n}$ cards, the last card discarded is the card numbered $6^{n}$.
$$
\begin{array}{l}
\text { Also } 6^{4}=1296<2016<6^{5}, \\
2016-1296=720,
\end{array}
$$

After discarding 720 cards, the card placed at the bottom is the one we are looking for.

When 700 cards are discarded, each 6 groups discard 35 cards, at this point, it is already the $700 \div 35 \times 6=120$th group. When discarding up to the 720th card, it is already the 2nd card of the 124th group, and the 3rd card is placed at the bottom. Therefore, the last card is the 3rd card of the 124th group.