Suppose that cards numbered $1, 2, \ldots, n$ are placed on a line in some sequence (with each integer $i \in [1,n]$ appearing exactly once). A move consists of interchanging the card labeled 1 with any other card. If it is possible to rearrange the cards in increasing order by doing a series of moves, we say that the given sequence can be rectified. Statements (37) The sequence 912345678 can be rectified in 8 moves and no fewer moves. (38) The sequence 134567892 can be rectified in 8 moves and no fewer moves. (39) The sequence 134295678 cannot be rectified. (40) There exists a sequence of 99 cards that cannot be rectified.
Suppose that cards numbered $1, 2, \ldots, n$ are placed on a line in some sequence (with each integer $i \in [1,n]$ appearing exactly once). A move consists of interchanging the card labeled 1 with any other card. If it is possible to rearrange the cards in increasing order by doing a series of moves, we say that the given sequence can be rectified.
Statements
(37) The sequence 912345678 can be rectified in 8 moves and no fewer moves.\\
(38) The sequence 134567892 can be rectified in 8 moves and no fewer moves.\\
(39) The sequence 134295678 cannot be rectified.\\
(40) There exists a sequence of 99 cards that cannot be rectified.