有趣的数学【02】:八卦与数学

in steempress •  14 days ago

小时候做过这样一道题,题目是:
将1,2,3,4,5,6,7,8,9九个数字填入下面的方格里,使得每横行,竖行和对角线上的三个数的和都相等。
image

当时我是一顿乱试,搞了很长时间,结果也没做出来。

老师出现了,告诉我一个口诀,说是古人的智慧,叫做《九宫诀》,内容是这样的:

二四为肩,
六八为足,
左三右七,
戴九履一,
五居中间。

照着这个口诀填写,就是标准答案。因为古人写字是从右到左的,所以“二四”,“六八”也要从右往左写,就变成了这样(九宫格的上面左右2个角是肩膀,下面两个角是脚丫):
image

当时觉得很神奇,一道数学题竟然能用一首诗来解决。

再大一点以后,才知道,这个九宫诀是古人用八卦看风水的总结,四正东、西、南、北和四隅东北、东南、西北、西南分别对应着数字及八卦,图是这样的:
image

当时就觉得古人老牛逼了。

再后来,看到了九宫格的题目有了扩展,各种各样的都有,其实都是从这个最基本的1~9的数字九宫格变幻出来的。

我们还是先观察基本九宫格,可以看出以下规律:

1~9是等差数列,差值为1,中位数是5;那么,

  1. 中位数放中间,
  2. 最小的放正下方,
  3. 最大的数放正上方,
  4. 第二大的放左下角,
  5. 第三大的放右边,

然后根据中间一列的和,就可以求出别的格子里面放什么数字了。


掌握了这个规律,比如:1,4,7,10,13,16,19,22,25填入九宫格,使得每横行,竖行和对角线上的三个数的和都相等,这又该怎么做呢?

我们来分析一下这个数列,它也是等差数列,差值为3,中位数是13,最大的是25,第二大是22,第三大是19,这些值按照上面的规律,填入九宫格中,是粗黑笔画的数字,剩下的根据每一行的和相等,就可以算出来了:
image

怎么样,下次在看到类似的九宫格的题目,会做了吧?

我发现,启蒙老师很重要。像我小时候这位数学老师就很好,他用生动的语言吸引了我,让我爱上了数学,享受数学的同时牢牢记住了这些技巧。

像这篇文章,我就没有查阅任何资料,全凭着小时候的记忆写出来了,谢谢那位老师!


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