Sudoku Cube

A scrambled colorless Sudoku Cube

The Sudoku Cube or Sudokube is a variation on a Rubik's Cube in which the aim is to solve one or more Sudoku puzzles on the sides or rows. The toy was originally created in 2006 by Jay Horowitz in Sebring, Ohio, and has since been the inspiration for several similar products and variations.

Production

The Sudoku Cube was invented by veteran toy maker Jay Horowitz. Horowitz first encountered the original Sudoku puzzle when a woman sitting next to him on a plane ride explained it to him. On the same plane ride, Horowitz had the idea of combining it with the Rubik's cube. He worked for a month with help from toy buyer Ken Moe until he figured out how to combine them together, and then when he figured it out, he "did not sleep for three days" while he worked out how to best arrange the numbers to create 18 unique Sudoku puzzles within the cube. Horowitz already owned molds to produce Rubik's Cubes, as he owned the Ideal Toy Company which had produced them in the past and he was able to use them to produce his new design. Horowitz then patented the numerical design that he created. Mass production was completed in China by American Classic Toy Inc, a company belonging to Horowitz. The product was sold in the United States in retailers such as Barnes & Noble and FAO Schwarz and sold for $9.87 each (a price chosen because each number appears once).

Marketing

Horowitz promoted his new product online, in magazines, in newspapers, and at toy fairs such as the 2007 American International Toy Fair and Hong Kong Toys and Games Fair, and on TV with English and Spanish commercials and demo videos. Adrienne Citrin, the spokeswoman for the Toy Industry Association, mentioned that Sudoku fans who felt like they had mastered the original paper version of the puzzle were interested in the new product. The product was originally launched in the US and then sold internationally, exporting to Spain, France, South Africa and the United Kingdom. Shortly after release, there were several imitator products sold on Amazon under the name "Sudokube".

Objectives

In a standard Rubik's Cube, the player must match up colors on each side of the cube. In the standard Sudoku, the player has to fill the grid with the digits 1-9 such that no digit is repeated in any of the rows, columns or squares. In the original Sudoku Cube, the player has several different objectives, some of which are borrowed from the original Sudoku puzzle, and one of which is borrowed from the original Rubik's Cube. The Sudoku objectives are mostly organized from levels 1-9, and are categorized into beginner (levels 1-3), intermediate (levels 4-6), advanced (levels 7-8) and master (level 9):

Beginner

Levels 1-3 all involve solving a number of sides. A side is considered solved when it contains each one of the digits 1-9 in the correct orientation:

• Level 1: Solve any one side
• Level 2: Solve any two sides
• Level 3: Solve any three sides

Intermediate

The intermediate levels are similar to the beginner levels, but involve solving more sides:

• Level 4: Solve any four opposite sides
• Level 5: Solve any five sides
• Level 6: Solve all six sides

Advanced

The advanced levels also include solving vertical columns and horizontal rows. A vertical column is considered complete when the digits 1-9 are in a vertical column on three contiguous sides of the cube. Likewise, the horizontal row is considered complete when the digits 1-9 are in a horizontal row on three contiguous sides of the cube:

• Level 7: Solve at least one vertical column and one horizontal row, which have a digit in common, and one side.
• Level 8: Solve two vertical columns and two horizontal rows and, which all have at lease one digit in common, and two sides.

Master

The master level involves solving all 18 Sudoku in the cube:

• Level 9: Solve all six vertical columns, six horizontal rows and six sides

Color Cube

In addition to the objectives derived from the Sudoku puzzle that use the numbers inscribed onto each sticker of the cube, the stickers are also colored such that the puzzle can also be solved like an original Rubik's Cube.

Variations

Official variations

A Sudoku Cube key chain version was released, which was smaller and cheaper - selling for $3.97 + $3.49 shipping.

Following the success of the Sudoku Cube, Horowitz created two more Sudoku products: The Sudoku Slide and The Sudoku Solitaire.

Unofficial variations

Colorless

Colorless Sudoku Cube

A colorless Sudoku cube removes the different colors from the cube, meaning the only objective is to place the digits 1-9 on each side, in the correct orientation.

Numberless

A numberless Sudoku cube removes the numbers entirely and uses colors to form the Sudoku challenge. The cube contains nine different colors, and the objective is to place one of each color on each side.

Different sizes

2×2×2 and 4×4×4 Sudoku cubes have also been created and mass produced, also with various colorless and numberless variations.

Molecube

Molecube

The molecube is a further variation on the numberless Sudoku Cube created by Uwe Mèffert, which has spherical pieces.

V-Cube Sudoku Cube

V-Cube created a variation which contains nine digits on each sticker, meaning that each side contains eighty-one digits in a 9×9 configuration. The goal of this puzzle is to complete a traditional 9×9 Sudoku on each side.

Solving technique

There are several techniques used to solve the Sudoku Cube and its variations.

Reduction

A technique common to all Sudoku Cubes is to split the problem into finding the configuration of the pieces, and the mechanics of solving the cube. It is assumed that the solver already understands the mechanics of solving the cube, and therefore the problem is reduced into finding the configuration of the pieces.

2 dimensional net

Sudoku cube net

A common technique for finding the configuration of the pieces it to map the three dimensional Sudoku Cube onto a two dimensional net. This allows for easier visualization of the pieces, and makes it easier to see the constraints that hold each piece in a separate position.

Corners first

The corners first approach involves solving the corners of the 3×3×3 Sudoku Cube like a 2×2×2 Sudoku Cube. This is an easier problem to solve, but makes solving the edges of the cube significantly easier.

Orientation

The requirement for the numbers on the Sudoku Cube to be oriented the same direction as the other numbers on the side significantly restricts which pieces are able to border each other. This allows for deductive reasoning which can be used to find which pieces must border each other, and hence how the cube must be solved.

Computer simulations

3-D programming languages such as VPython can be used to create simulations of a Sudoku Cube. Such simulations can offer features such as scaling the Sudoku Cube (to create 4×4×4 or 5×5×5 puzzles), saving, resetting, undoing, and the option to design one's own Sudoku Cube patterns.

See also

• Combination puzzles
• Mechanical puzzles