11. On an infinitely large chessboard, there is 1 chess piece on a small square, where each small square is $1 \mathrm{~cm} \times 1 \mathrm{~cm}$. The chess piece moves according to the following rules:
(1) On the 1st move, the chess piece moves one square north.
(2) On the $n$-th move, if $n$ is odd, the chess piece can choose to move north or south; if $n$ is even, the chess piece can choose to move east or west.
(3) On the $n$-th move, the chess piece moves $n$ squares in the same direction.

After moving the chess piece 12 times, make the distance between the center of the final square and the center of the initial square as small as possible. What is the minimum distance? $\qquad$ cm.
11.2.

All even-numbered moves are along the east-west direction, while all odd-numbered moves are along the north-south direction. The piece has traveled a total of $36 \mathrm{~cm}$ along the east-west direction and $42 \mathrm{~cm}$ along the north-south direction. The displacement along the east-west direction can be $0(1+3+5-7+9-11)$, but the displacement along the north-south direction cannot be 0; otherwise, the total distance traveled should be divisible by 4, and 42 leaves a remainder of 2 when divided by 4.

In fact, the displacement along the north-south direction can be $2 \mathrm{~cm}$ $(2+4+6-8+10-12)$.