If a puzzle has exactly one block, the puzzle is either:
- Unsolvable, or
- Solvable in 0 moves, or
- Solvable in 1 move.
If a puzzle has two blocks, it can already take an arbitrary number of moves to solve. For instance, consider the following start- and goal-configuration:
++++............
+A.+............
................
..............A.
This takes 25 moves to solve, because the blocks A and + need to be moved alternatingly one position to the right. If you don't demand the blocks to be connected, this can even be simplified to a single line each:
+A.+............
..............A.
Another example, based on a different idea, looks like this:
.............................
bbbbbbbbbbbbbbbbbbbbbbbbbbbbb
b b b b b b b b
bA..b...b...b...b...b...b...b
b b b b b b b b b
b.b...b...b...b...b...b...b.b
bbbbbbbbbbbbbbbbbbbbbbbbbbbbb
.............................
.............................
. . . . . . . .
...........................A.
. . . . . . . . .
.............................
.............................
Here, the block b must be moved up and down alternatingly, while block A moves two positions to the right at a time.