"Clever Toys" is a puzzle company in the Czech Republic.他们的网站描述五种不同的手工,木制拼图魔方相关的数学。

Contents

谜题

这是照片拼图的“三人组”。

Here is an English translation of their description.

这2 d游戏的任务是把所有的椭圆根据他们的颜色到一个基本的组装。通过移动的球槽和中心轮,你可以逐渐得到每一个球,你需要它。

I am not sure that Clever Toys is still in the business. They have not responded to my emails and I have not had been able to purchase an actual price puzzle. Of course, that is all the motivation I need to make a MATLAB model.

模型

这是初始配置。有三个固定外,部分,光盘和一个内心,满,光盘。每个外部光盘包含10个频道。当内部盘定位得当,一个通道可以旋转的玻璃球。旋转内椎间盘本身移动一些,但不是全部,玻璃球,从而加扰的颜色。

Like Rubik's Cube, the objective of the puzzle is to return to this initial state "solved".

Mathematically, both Rubik's Cube and price are ultimately -based upon rotation matrices. The Rubik 's Cube is a 3 D puzzle whose state is specified by the position and orientation of 27 cubelets;This gives Rubik's Cube about4.3 * 10 ^ 19Possible positions. At each step, there are six faces and 12 possible rotations.

The price is a 2 - D puzzle whose state is specified by the colors of the marbles. There are 10 marbles of each of three colors;This the implies that for any partial or from30!/ (10!^ 3 = 5.6 * 10 ^ 12可能的位置。在每个步骤中,有八个可能的旋转,四盘,顺时针或逆时针。

争夺

“争夺”是一个整数向量元素之间4 + 4,指定移动或旋转。移动0初始化模型。移动dwithd1、2或3旋转所有的弹珠d- th channel counter - clockwise for one - tenth of a full rotation. The Movedwithd1、2或3是相应的顺时针旋转。移动4和4把中央盘顺时针或逆时针三分之一的一个完整的旋转。这旋转一些,但不是全部,大理石和混合的颜色。

Here is a scramble of length 29 that provides our example.

D = [4 1 3 1 1 2 3 1 4 4 2 4 4 3 2 3 3 2 1 1 3 4 2]

And here is the scrambled the result.

动画

This animated GIF shows the scrambling process one move at a time. The animation does not repeat automatically, so to start it over again and refresh your browser. If it still doesn 't move, find another browser.

解读

Reverse the scramble by running it backwards, changing the sign of the each move. This will return the scrambled the position to the initial position. I call This "unscramble";It solves the scrambled the position by a "follow the breadcrumbs" algorithm.

这两个动画需要很长时间才能和我的浏览器运行——大约80秒。

金宝搏官方网站

I don 't have any idea about how to later solve a given position without using the knowledge of how it was, and I don' t have any idea about how to quantify the difficulty of finding a solution. This is in sharp contrast to the Rubik 's Cube where there are measures of difficulty and algorithms for finding optimum so金宝搏官方网站lutions.

软件

这个程序可以在This link是互动的。点击或alt-click在任何的四个光盘盘采取行动。

谢谢

Thanks to Steve Eddins and Tom Lane for help with this post.

得到了MATLAB代码

Published with MATLAB ® R2022b