Despite the onslaught of computer and video games designed to exercise spatial cognition, three hand-held manipulative puzzles remain popular: *Rubik’s Cube*, by Winning Moves, celebrating its twenty-fifth anniversary this year; the *Retro Bedlam Cube*, by Bedlam Puzzles, Ltd.; and Thinkfun’s modern rendition of the ancient *Gordian’s Knot*.

*Rubik’s Cube* has been a cultural icon since its initial craze in the 1980s. The standard *Rubik’s Cube* is a 3x3x3 inch box made up of twenty-six visible interlocking cubes that rotate on a central axis. The small cubes are color-coded and set up in rows of three. Each of the cube’s eight corner pieces has three colored sides, while each of its twelve edge pieces has two colored sides; the cubes in the center of each of the puzzle’s six faces have only one colored side.

The object of the puzzle is to move rows of three in one-quarter, one-half, or three-quarter turns, horizontally and vertically, until each of the six sides is a solid color. The trick is to line up colors on one face without displacing their alignment on other faces. Success relies on cognitive spatial and tactile manipulative skills, taking into account the location and movement of smaller cubes with one-, two-, or three-colored sides.

Created in the late 1970s by Hungarian professor of architecture and design Erno Rubik, the cube had sold over a million copies worldwide by 1982. The craze waned by the 90s, but thousands of cube clubs and competitions like those sponsored by California Institute of Technology have contributed to its current popularity. Literally millions of web sites tout an equal number of possible solutions, some challenging puzzlers to create geometric patterns rather than solid colors on the cube faces. Higher-level mathematical studies analyze the *Rubik’s Cube’s* application of algebraic group theory and use of algorithms (see sidebar), useful perhaps for mathematically gifted high school students, but one doesn’t need to understand complex theory to enjoy the puzzle and exercise cognitive spatial skills.

The *Retro Bedlam Cube* is another popular retro, three-dimensional manipulative that relies on spatial awareness. Based on the 1982 creation of British inventor Bruce Bedlam, The *Retro Bedlam Cube* consists of thirteen separate, interlocking, polycubic shapes that fit together inside a clear plastic 4x4x4 inch box. The pieces come in three colors, though color is not a factor in solving the puzzle. The object is to reassemble the three-dimensional geometric shapes inside the clear cube, a feat with over 19,000 possible combinations, none of which is easy or obvious. Solving the puzzle is a trial-and-error endeavor that enhances spatial awareness and hand-eye coordination.

Like *Rubik’s Cube*, The *Retro Bedlam Cube* has a large following of devotees who join clubs and enter contests sponsored by numerous web sites. There’s even a limited edition golden cube purchase for anyone who comes up with a previously undiscovered solution. Several novelty varieties of the game area available through the British Bedlam Company, including solid colored cubes and the *Egglam Bedlam Cube*, all white except for one yellow piece.

The *Retro Bedlam Cube* and the Bedlam Company varieties are excellent options for gifted middle school students and for students who learn best through tactile manipulation. The puzzle, however, is quite difficult and can be frustrating. “** Bedlam Cube Solver**,” by Daniel Tebbutt, offers color-coded solutions, showing three of the six sides of the cube. Even with the diagrams, however, puzzlers still have to use spatial cognition in reassembling the cube.

The latest variation of cube puzzles is Thinkfun’s *Gordian’s Knot*. Based on the ancient story of Midas’ famous knot that Alexander the Great unraveled as the source of his power, *Gordian’s Knot* consists of six interlocking, color-coded puzzle pieces that the puzzler must unravel. Each slide of a puzzle piece allows another piece to slide, though not every move is a correct one. A series of sixty-nine correct moves releases the pieces, one at a time, until the knot is unraveled. The second challenge is to put them back together again.

Working the puzzle requires spatial cognition, manual dexterity, and patience. Some of the moves require holding one piece in place while moving two other pieces at the same time. Unlike The *Retro Bedlam Cube*, which has thousands of possible solutions, *Gordian’s Knot*has only one correct sequence of moves. Solving the puzzle can be frustrating, but for those who need help, a detailed instruction booklet for both taking the puzzle apart and reassembling it is included in the package.

*Gordian’s Knot* was selected by *Games* magazine as best puzzle of the year for 2006. Suggested for children eight and up, it is appropriate for gifted elementary and middle schoolers as well as adult puzzle enthusiasts.

*—Sarah Boone, MA, MFA*

*Sarah Boone holds a master’s degree in teaching and is certified in gifted education. She has an MFA in creative writing, which she teaches at North Carolina State University.*

###### Product Information

**Rubik’s Cube****Retro Bedlam Cube****Gordian’s Knot**

All puzzles are available for about $10-12 online and in educational toy stores.

###### Additional Resources

See David Joyner’s *Adventures in Group Theory: Rubik’s Cube, Merlin’s Machine & Other Mathematical Toys* (John Hopkins, 2002) and Richard Koff’s “**Finding Optimal Solutions to Rubik’s Cube Using Pattern Databases.**” UCLA, 1997

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