Details

The search generates all solutions that are distinct up to a rotation of the cube as a whole. There are 480 such solutions. The first piece is placed in one of four positions; the remaining pieces are tried in all possible translations and rotations. It turns out that only the first placement of the first piece admits any solutions, due to parity considerations.

The first control triggers a single step of adding another piece or removing one piece when backtracking. The second control runs the animation until a solution is found. It introduces a variable delay after each step. The third control continues the search to completion and introduces delays only when a solution has been found. Clicking a control again stops the animation. The two counters count the number of solutions found and the total number of steps tried.

The natural search algorithm is recursive. To allow single-stepping and maintaining state in the notebook, it was converted into an iterative version.