此类问题涉及Dominos是否有名字?

发布于 2025-02-11 03:49:50 字数 384 浏览 0 评论 0原文

我的教授向我展示了我认为很有趣的问题。

问题如下: 如果您有一个2^n x 2^n棋盘,然后从中卸下一个正方形,您是否可以用L形trominos填充它?

答案是肯定的,我认为有趣的方法。

示例

在此示例中,x是删除的正方形,数字表示L-的形状形状的trominos。在Checkerboard的每个可能的置换中,应该有一个解决方案,可以用Trominos填充每个正方形。

有谁知道这种问题是否在数学领域中命名?我想了解更多有关这些的信息。

我还将尝试编程,任何人都有任何有帮助的想法?

There's this problem that my professor showed me that I thought was interesting.

The problem is as follows:
If you have a 2^n by 2^n checkerboard and remove one square from it, will you be able to fill it with L-shaped trominos?

The answer to this is yes, the method of which I thought was interesting.

Example

In this example, X is the removed square and the numbers represent the shape of the L-shaped trominos. In every possible permutation of checkerboards, there should be a solution to fill up every square with trominos.

Does anyone know if this kind of problem is named in a field of math? I'd love to learn more about these.

I'm also going to attempt to program this, anyone have any ideas that could help?

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旧伤慢歌 2025-02-18 03:49:51

有一个广泛的问题家族称为 平铺问题 ,询问何时,以及如何使用固定的数字集合来拼贴不同的形状。

关于 图细分 的其他问题,问题是何时,或如何将一些较大的图形分成各种形状的较小图形。

There's a broad family of problems called tiling problems that ask when, whether, and how to tile different shapes using a fixed collection of figures.

There are other questions about figure subdivisions, where the question is when, whether, or how to subdivide some larger figure apart into smaller figures of various shapes.

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