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第123章 密室:笔记与黄印(1 / 2)

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“你不是……”张恒峰欲言又止。

看见何克钦直接伸手拿过纸条时,张恒峰就想吐槽“你不是有洁癖吗”,但一想到何克钦那句“大家与其关注我的私事”,他还是硬生生将后半句话咽了回去。

何克钦当作没听见,把纸条放下。

他拿纸条的姿势有些许怪异,只用手指尖端握着纸条一角,似乎手掌无法完全张开。

“自我描述数,一种可以通过数字本身描述该数字自身特征的数字。”何克钦解释道:“我曾经遇到过类似谜题,因此这才能很快想到。”

张恒峰看了看数字,挠头道:

“它怎么描述自身特征?”

何克钦平静道:

“你看,第一个数字是2101。

“它的第一位数字是描述这串数字里‘1’出现的个数。这串数字里‘1’一共出现了两次,因此它第一位数字就是‘2’。

“它的第二位数字是描述这串数字里‘2’出现的个数,由于‘2’只出现了一次,所以它的第二位数字是‘1’。

“以此类推,直到最后一位数字,它描述的是这串数字里‘0’出现的次数。”

张恒峰听得似懂非懂,看向第二个数字。

“哦……第1位的2代表这串数字里有2个1,第2位的1代表这串数字里有1个2,第3位的1代表这串数字里有1个3……”张恒峰一拍脑袋。“我懂了,原来如此!”

“它的每一位数字都代表了这一位置的数字在整个数中出现的次数。”柳茹芸若有所思地总结道。“最后一位数字则代表了0这个数字在整个数中出现的次数。”

“正是如此。”何克钦点头道。“而十位数的自我描述数,只有一个。”

所有人都看向了他。

“首先,由于每一位数字都代表该数字出现的次数,所以将这些数字相加,结果就是这个数字的总位数。”何克钦说着显而易见的结论。

2101是四位数,四个数字相加的结果是4;是七位数,七个数字相加的结果是7。

而保险柜的密码是十位数,因此其所有数字相加的结果一定是10。

“这也意味着,这个十位数中,6、7、8、9这四个数字最多出现一个。”何克钦笃定道。“而且只会出现一次。”

否则,一旦这四个数字出现了任何两个或两次,最终十个数字相加的结果就超过了10。

“另一个结论是。”柳茹芸微笑附和道。“这个十位数的大多数字都是0。”

否则十个数字相加的结果也会超过10。

何克钦点头道:

“两个结论结合起来,6、7、8、9中出现且仅出现一次的那个数字,就代表着0的数量。”

推算到了这一步,虽然也可以继续整理逻辑,但直接分类讨论会更加简单。

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