17camels and 3 sons 17隻駱駝與3個兒子

 |2016.01.31
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提 要

常聽到數學老師說:「別鑽牛角尖……」;進入職場後,可能會聽到老闆說:「think outside the box……」(跳脫框架思考)。在電影《大英雄天團(Big Hero 6)》的天才主角創意枯竭時,被哥哥翻過來抱、換個角度觀察,然後就創出不得了的發明。

換個角度、跳脫框架,正是解決問題的方法。

Long long ago, there lived an old man with his three sons in a deserted village, located in the vicinity of a desert. He had seventeen camels, and they were the main source of his income. He used to rent out camels as means of shipping in the desert. One day, he passed away and he had a will, leaving his assets for his three sons.

After the funeral and the other obligations were over, the three sons read the will. While the old man divided all the properties he had into three equal parts, he divided the seventeen camels in a different way. It wasn't shared equally among the three as "seventeen" is an odd number and prime number, which cannot be divided.

The deceased old man stated that the eldest son will own half of the seventeen camels, and the middle one will get the one-third of the seventeen camels, and the youngest one will get his share of camel as one-ninth!

All of them were stunned to read the will and questioned how to divide seventeen camels as mentioned in the will.

It is neither possible to divide seventeen camels and give the half of the seventeen camels to the eldest one, nor able to divide the camels to the other two sons. They spent several days to divide the camel as mentioned in the will, but none could find the answer.

They finally took this issue to the wise man in their village. The wise man heard the problem and instantly found a solution. He asked them to bring all seventeen camels to divide them as intended by their father.

The sons brought the camels to the place. The wise man added a camel owned by him and made it count eighteen.

Then, he asked the first son to read the will, he get half the eighteen camels, which now counts to nine camels! The eldest one got nine camels as his share.

Remaining camels left nine camels.

The wise man asked the second son to read the will, he was assigned a share of one-third of the total camels.

It comes to six camels, therefore the second son got six camels as his share.

Then the third son read his share of camel one-ninth of total eighteen camels, so the youngest one got two camels as his share.

Totally there were 9 + 6 + 2 camels shared by the brothers, which counts to seventeen camels.

One camel brought by the wise man was taken back.

The wise man solved this problem smartly with his intelligence, intelligence is nothing but finding a common ground to solve an issue.

The three sons fulfilled their father's will and learned, every problem has a solution.

解 說

很久很久以前,有一位老人與他的三個兒子,住沙漠附近的一個荒蕪的村莊。老人的十七隻駱駝,是他主要收入來源,他出租駱駝當作「沙漠之舟」。有一天,他離開了人世,他留下遺囑表示,他的資產分給他的三個兒子。

葬禮以及其他儀式都結束之後,三個兒子讀老人的遺囑。老人將所擁有的「財產」──十七隻駱駝,「按比例」分給三個兒子,但是,「十七」是奇數也是質數,「按比例」平分,簡直是「不可能的任務」。

老人在遺囑上說,大兒子可以得到自己十七隻駱駝的一半,二兒子可獲得駱駝總數的三分之一,最小的兒子會得到他全部駱駝的九分之一!

三個兒子讀完老人的遺囑,都被驚呆了,議論紛紛究竟要如何「按比例」平分這十七隻駱駝。

既然「十七」不可能均分,所以分十七隻駱駝的一半給大兒子不可行,當然也就沒辦法分駱駝給另外兩個兒子。他們花了好幾天研究遺囑中的數學難題,但沒有人能找到答案。

終於,他們決定把這個問題交給他們村里的智者。智者聽到這個問題,立即找到了解決的辦法。他要求他們三個把十七隻駱駝全部帶來,他能夠用他們父親所希望的方式「按比例」平分。

三個兒子把駱駝都帶來之後,智者在駱駝群中加入一隻他自己的駱駝,使牠們湊成十八隻。

然後,他要求最年長的兒子讀老人的遺囑:「大兒子可得到駱駝的半數」,十八隻的半數也就是九隻駱駝,於是長子得到九隻駱駝。

大兒子分完之後,還剩餘九隻駱駝。

智者要求二兒子讀爸爸的遺囑:「二兒子可獲得駱駝的三分之一」。

十八隻的的三分之一是六隻駱駝,所以第二個兒子拿到了六隻駱駝。

「最小的兒子會得到他全部駱駝的九分之一」,於是第三個兒子根據爸爸的遺囑,得到十八隻駱駝的九分之一,也就是兩隻駱駝。

三個兄弟分別得到九隻、六隻、兩隻駱駝,三個人分到的駱駝加起來,不多不少正好十七隻 。

多出來的一隻、智者「提供」的駱駝,由他自己帶回家。

智者果然是聰明人,巧妙地用他的智慧,找到共同點略為變通,就解決了這個「數學難題」。

三個兒子開心地履行了父親的遺願,同時也學到了:「每一個問題,都有解決方案」。

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