Problem 766
Sliding Block Puzzle
A sliding block puzzle is a puzzle where pieces are confined to a grid and by sliding the pieces a final configuration is reached. In this problem the pieces can only be slid in multiples of one unit in the directions up, down, left, right.
A reachable configuration is any arrangement of the pieces that can be achieved by sliding the pieces from the initial configuration.
Two configurations are identical if the same shape pieces occupy the same position in the grid. So in the case below the red squares are indistinguishable. For this example the number of reachable configurations is $208$.
Find the number of reachable configurations for the puzzle below. Note that the red L-shaped pieces are considered different from the green L-shaped pieces.
滑块谜题
滑块谜题是一种在指定范围内滑动滑块以达成特定布局的谜题。在本题中，我们要求滑块每次向上、向下、向左或向右滑动时，必须移动单位距离的整数倍。
从初始布局出发，通过滑动滑块所能达成的布局统称为可达布局。
如果两个布局中，所有相同形状的滑块均占据相同的位置，则视为相同的布局。如下图所示，所有由红色标记的正方形滑块都是不可区分的，最终以此为初始布局的可达布局共有$208$种。
求以下图为初始布局的可达布局的总数。注意，由红色标记的L形滑块和由绿色标记的L形滑块应视为不同形状的滑块。