36 cube

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36 Cube in the unsolved state

Cube 36 ( English for 36 cubes ) is a three-dimensional puzzle by the company Inc. ThinkFun the riddle by the mathematician and inventor Derrick Niederman was invented. It was designed and constructed by the German designers Holger Burckhardt and Wolfgang Baier. It consists of a base board with slots and different heights of colored bars. The puzzle was first presented on the German market in February 2009. It was named Top Ten Toys 2009 by the Federal Association of Toy Retailers e. V. excellent.

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. Also included are colored sticks that can be picked up by the guide pins on the base plate. The color bars are grouped by six different hues (red, yellow, blue, green, purple and orange). There are six sticks for each color group, making a total of 36 color sticks. The task is to solve the puzzle in such a way that each color appears only once in each row and in each column. The special feature is that both the guide pins on the base plate and the colored bars are of different heights within six different levels. The puzzle must be solved in such a way that the surface forms a uniform level at the end. Therefore, the game has similarities with the logic puzzle Sudoku , with the difficulty being expanded to include a three-dimensional playing field.

Terms

  • Color stick : The color stick has one of the six colors red, yellow, blue, green, purple and orange. In addition, it differs through six different height levels.
  • Guide pin : A guide pin is arranged on the square base plate and accepts one colored stick. It practically forms the counterpart to the color stick and can assume one of six different height levels.
  • Base plate : The base plate has a square shape and houses 36 guide pins.

Solvability

In the game instructions it is pointed out that there is a solution, although it is very difficult to find. The designers suspected 6 solutions. At first glance it looks as if each of the six heights is represented once in all rows and in all columns. One solution for such a base plate would be a 6x6 Greco-Latin square . Leonhard Euler already suspected with his problem of 36 officers that there was no solution for this size; this was confirmed in 1901 by Gaston Tarry .

But that was precisely the starting point for the inventor Derrick Niederman. In order to better understand the problem of 36 officers for his students, he came up with the idea for the 36 Cube. And he had the "mean" idea to use a puzzle trick to find a solution:

There is more than one solution for the 36Cube. In contrast to the other games from Thinkfun Inc., the 36Cube was not referred to as a thinking and logic game, but as a puzzle. The prerequisite that the heights are different in each row and in each column does not come true on closer inspection. In fact, there is a guide pin for height 6 color bars that also fits a certain height 5 color bar. In turn, a certain height 6 color stick will fit on a guide pin for height 5. Taking this trick into account, it is possible to solve the puzzle.

See also

Individual evidence

  1. ↑ Cliquenabend.de: In the test: 36 Cube , test report from May 26, 2009
  2. ↑ Press release from the Federal Association of Toy Retailers e. V. (PDF; 29 kB)
  3. ↑ Maths Planet: The Problem of the 36 Officers

Web links