Bedlam Cube Demonstration Software
The Bedlam Cube (or Crazee Cube) is a so-called solid dissection puzzle invented by the British puzzle expert Bruce Bedlam.
The puzzle consists of thirteen polycubic puzzle pieces that form together, if correctly assembled, a solid cube without any hollow spaces. Twelve puzzle pieces consist of 5 basic cubics and one piece consists of 4 basic cubics – yielding a total of 64 basic cubics, which results in an assembled 4 x 4 x 4 cube.
There are 19186 unique ways to assemble all pieces to a box, excluding all rotational copies.
For software download click here: DOWNLOAD cube_pkg.exe
The software is developed as a MATLAB stand-alone application and runs on Microsoft Windows XP 32 operating system. It might also run on other Microsoft Windows versions.
Adobe Acrobat Reader or another software capable of reading pdf files must be installed on the target computer.
For installation, copy file cube_pkg.exe into a folder of your choice on your computer’s hard disc. Double click the file in the destination folder and follow the steps of the InstallShield Wizard for installing the MATLAB Component Runtime. If during installation the program issues a warning that the .NET Framework is not installed on your computer, click OK (do not install the .NET Framework).
In order to launch the game after installation has completed, double click file cube.exe.
The player needs to tile all 13 puzzle pieces into the box so that they eventually form a cube. Puzzle pieces are selected by the player by clicking their selection button. It is mandatory that the selected piece fits into the box with the already tiled pieces (if any), covering the next empty basic cubic (the next tiling position). The software will not allow for any deviation from this rule.
Additionally, the software provides for several supporting features.
If chosen, the computer can help the player in manually selecting a puzzle piece, preventing from any tiling configurations that do not lead to a fully assembled cube. Furthermore, the computer can take over full control over piece selection.
Depending on the player’s selection, the software indicates the next mandatory tiling position inside the cube and/or the tiling position of the last tiled puzzle piece.
If it is possible to place the last tiled puzzle piece differently into the box than shown in the visualization, the player may choose between these alternative tilings before proceeding with the next puzzle piece.
If, at any stage, the player changes his mind or endures difficulties, he may remove the last tiled piece from the box (until the box becomes empty) or reset the box to the game’s initial position.
For a better visualization, the player may turn around the 3-D view of any of the puzzle pieces or the whole box.
If wished, the player may deviate from the piece-by-piece tiling procedure and may place all 13 puzzle pieces at once into the box.
Messages and hints are displayed in the message line.
Figure 1: Overview of Displays and Controls
After launching the software, a window as shown in Figure 1 comes up with mode “player (PC aided)” selected. In this default mode, the computer assists the player when putting piece after piece into the box. The next position within the box that needs to be covered by the next piece to be put into the box (next tiling position) is visualized in transparent green color (item 9 in Figure 1).
The next tiling position is the next empty basic cubic (out of a total of 64 basic cubics of the whole box) following the tiling order. For understanding the tiling order, one has to imagine the box as a 3-D coordinate system with X, Y, and Z axes as shown in Figure 2. The tiling order is first X, then Y, and finally Z. In other words – first, at the bottom of the box at Y position 1, all empty X positions from 1 to 4 has to be covered in this order by puzzle pieces. Then, this procedure repeats at Y position 2; then at Y position 3; and finally at Y position 4. Once all 16 X by Y positions at the bottom of the box are filled with puzzle pieces, one has to move up to the next Z layer and repeat everything until all 64 X by Y by Z basic cubics of the box are filled with all 13 puzzle pieces.
This tiling order resembles the real-world procedure of solving the Bedlam cube. Neither the player nor the computer can deviate from the tiling order. It is not possible to put a puzzle piece at an arbitrary place inside the box without covering the next tiling position.
Figure 2: Explanation of Next Tiling Position
To put a piece into the box, the player needs to click the piece selection button to the left of the depiction of the according piece (item 3 in Figure 1). The depiction of a piece that was successfully put into the box disappears next to the piece selection button and shows up inside the box (see Figure 3).
In case there are more ways to put the just placed piece into the box, the control for selection of alternative tilings (item 12 in Figure 1) is enabled (see Figure 3). The currently selected and the maximum numbers of these alternative tilings (items 15 and 16 in Figure 3) are shown. Using the forward and backward arrows (items 17 and 14 in Figure 3), an alternative tiling may be chosen. Alternatively, a piece fitting might be selected by overwriting the currently selected number with the desired one and hitting the Return key.
In default mode, only those alternative piece fittings are enabled that allow for solving the whole puzzle when proceeding from the current piece configuration inside the box.
Figure 3: Selection of Alternative Piece Fittings
If it is not possible to fit a piece into the box (with or without already tiled pieces) covering the next tiling position, an according message line (item 4 in Figure 1) appears and the corresponding piece selection button is disabled. Furthermore, in default mode, the computer prevents the player from placing pieces into the box that lead to configurations which do not allow for solving the whole puzzle, although it might be technically possible to fit the according piece into the box at the tiling position.
In order to get a better comprehension of the pieces’ shapes and there positions inside the box, the player might turn around the 3-D depiction of a piece or the box by placing the cursor over the item to be turned, clicking and holding the left mouse button, and dragging the mouse. Double clicking the turned item returns it into its initial viewing angle.
At any time, the player may remove the last tiled piece one after another from the box by clicking button “Remove Last Piece!” (item 11 in Figure 1). Also, the box might be reset to its initial empty position by clicking button “Reset Box!” (item 10 in Figure 1).
In “PC” mode, the computer takes over full control of puzzle piece selection.
This mode is activated by selecting list item “PC” in the drop down menu “Piece Selection” (item 7 in Figure 1).
In this mode, the piece selection buttons are disabled and button “Have PC Fit Pieces(s)!” (item 13 in Figure 1) is enabled. By clicking this button, the computer puts the first fitting puzzle piece covering the next tiling position into the box. After that, an alternative piece fitting (if any) may be chosen by the player. Now, the next computer-selected puzzle piece is placed into the box by clicking once again button “Have PC Fit Pieces(s)!”. This procedure repeats until the box is fully tiled.
Contrary to mode “player (PC aided)”, in mode “PC” alternative piece fittings are shown for all possible remaining pieces, not only for the first fitting piece that was selected by the computer. In other words, in mode “PC” alternative piece fittings comprise all turning configurations of all remaining puzzle pieces that fit into the box, cover the next tiling position, and lead to a configuration that allows for solving the whole puzzle.
In “player only” mode, the player has full control of puzzle piece selection and tiling. There is no support by the computer. This is the mode that resembles closest the real-world procedure of solving the Bedlam Cube puzzle.
This mode is activated by selecting list item “player only” in the drop down menu “Piece Selection:” (item 7 in Figure 1).
As in mode “player (PC aided)”, the player needs to click the piece selection button to the left of the depiction of the according piece (item 3 in Figure 1) in order to put a puzzle piece into the box. After tiling a piece in the box, the player may choose between alternative piece fittings (if any) of the just tiled piece.
In case, the player-selected piece does not fit into the box covering the next tiling position, an according message is displayed in the message line and the piece selection button is disabled.
Contrary to modes “player (PC aided)” and “PC”, in mode “player only” puzzle pieces can be put into the box (providing they fit and the next tiling position is covered) even when they form a configuration that will not allow for solving the whole puzzle. Therefore, at a certain stage a configuration might occur where none of the remaining puzzle pieces can be tiled into the box. In this situation, all piece selection buttons of the remaining puzzle pieces are disabled and an according message is displayed in the message line. From here, the player may proceed by either choosing an alternative piece fitting (if any), removing the last or more tiled pieces, or resetting the box.
Contrary to tiling the box piece by piece, the software provides the option of solving the whole puzzle with all thirteen puzzle pieces at once where the first puzzle piece to cover the first tiling position is either selected manually by the player or automatically by the computer.
This option is activated by selecting list item “whole box at once” in the drop down menu “Tiling Method:” (item 6 in Figure 1). With this option activated, there are only two piece selection modes available: “player (PC aided)” and “PC”.
When mode “player (PC aided)” is active, the player needs to select the puzzle piece to cover the first tiling position by clicking its piece selection button. Doing that, the selected piece is put into the cube at the origin of the box and all other pieces are automatically added to fill the whole box. Alternative piece fittings include all possible configurations with the player-selected piece at the first tiling position. In this case, rotational copies of puzzle solutions occur. Therefore, the number of alternative piece fittings might be bigger than the total number of all unique puzzle solutions.
When mode “PC” is active, by clicking button “Have PC Fit Piece(s)!” the computer puts piece number 1 at the origin of the box and fills in all other remaining pieces. In this case, alternative piece fittings include all 19186 unique puzzle solutions without any rotational copies.
By selecting the according list item of drop down menu “Show Tiling Position:” (item 5 in Figure 1) the player may visualize either the position inside the box where to place the next puzzle piece, the position that was covered by the last tiled puzzle piece, both of them, or none of them.
Tiling positions are visualized in transparent green color either at the imaginary surface of an empty basic cubic in the box or at the skin of a basic cubic of an already tiled puzzle piece.
During the game, drop down menus and control buttons are only enabled when they make sense at the according stage with the combination of the selected mode and option.
When tiling the box piece by piece, the player may switch, if desired, during the game to another tiling control mode (drop down menu “Piece Selection:” – item 7 in Figure 1).
When the box is not fully tiled yet, it is always possible to switch between modes “player (PC aided)” and “PC”. It is also always possible to switch to mode “player only” from the other modes.
When switching from mode “player only” to one of the computer supported modes, however, it might occur that there is no way of solving the whole puzzle proceeding from the current piece configuration in the box. Therefore, in this case the computer checks if it is possible or not to solve the puzzle taking into account the already tiled pieces.
If it is not possible to solve the puzzle, an according message is shown and the mode is automatically reverted to “player only”.
If it is possible, however, to solve the whole puzzle with the assembled configuration, the new selected mode (either “player (PC aided)” or “PC”) is activated and the game can be continued in this mode.
When playing in mode “player only”, it might be a good tactical approach for the player trying to switch from time to time to a computer supported mode in order to check whether it is still possible to solve the whole puzzle continuing from the current piece configuration inside the box. In case, there is no way of solving the puzzle from the current stage, the player might want to either select an alternative piece fitting (if available) or remove one or more puzzle pieces and try putting another piece into the box.
Use of this software is permitted only by the author’s conditions. The author is the holder of all rights.
To get the conditions of use, or for any other question concerning the software or this Web presentation, contact the author by email: firstname.lastname@example.org