36 Cube

36 Cube (English for 36 dice ) is a three-dimensional puzzle of the mathematician and puzzle inventor Derrick Niederman, which consists of a base board with slots and different levels of color bars. The puzzle was first presented in 2009 to the German market. It has been awarded as Top Ten Toys in 2009 by the Federation of the Sporting Goods - Retail Trade.

Description

The puzzle consists of a square base plate made ​​of dark gray plastic that contains 36 guide pins. The guide pins are each arranged in six rows and six columns. Further, color bars are included, which can be taken up by the guide pins of the base plate. The color bars are grouped by six different colors ( Red, Yellow, Blue, Green, Purple and Orange ). For each color group, six bars are available, resulting in the total number of 36 color bars. The task is to solve the puzzle in such a way that each color both in each row and in each column occurs only once. The special feature is that both the guide pins of the base plate and the color bars within six different stages have different heights. The puzzle to be solved such that the surface at the end of which forms a single plane. Therefore, the game similar to the logic puzzle Sudoku, the difficulty of a three-dimensional field is expanded.

Terms

• Color bar: The color bar has one of the six colors red, yellow, blue, green, purple and orange. In addition, it differs by six different height levels.
• Guide pin: A guide pin is placed on the square base plate and each takes a color bar on. He is practically the opposite of the color bar, and can assume one of six different altitude levels.
• Base: The base plate has a square shape and consists of 36 guide pins.

Solubility

In the game's instructions should be noted that there is a solution, although this is very hard to find. At first glance, it looks as if each of the six levels in all rows and all columns are each represented once. A solution for such a base would be a Greco- Latin square of size 6x6 match. Already Leonhard Euler suspected with his problem of the 36 officers that for this size there is no solution; this was confirmed in 1901 by Gaston Tarry.

Nevertheless, there is a solution for 36 cube. The condition that the heights are different in each row and in each column, does not hold true on closer inspection. Indeed, there is a guide pin for color bars of height 6, the fits a certain color bar of height 5. In turn a certain color bar height 6 fit on a guide pin for height 5 Taking into account this trick it is possible to solve the puzzle.