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Work: 雉兔同籠 Viewing: Source

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雉兔同籠，又曰和尚分菓，可以二元一次方程算題也，出於孫子算經
。

原問

問今有雉、兔同籠，上有三十五頭，下有九十四足。問：雉、兔各幾何？

答雉二十三，兔一十二。

術一：上置三十五頭，下置九十四足。半其足，得四十七，以少減多，再命之，上三除下三，上五除下五，下有一除上一，下有二除上二，即得。

術二：上置頭，下置足，半其足，以頭除足，以足除頭，即得。

此為砍足法，中外之首創也。

凡例

問百和尚，分饃百，大和尚每人著三，小和尚三人著一，問大小和尚各若干人?

答大和尚二十五人，小和尚七十五人。

法大和尚一著三，小和尚三著一，相加即四和尚食生菓，以四除一百，得二十五為大和尚數，餘即小和尚數也。

據

簡明珠算 陳湘記書局 民國廿七年版

孫子算經

《數學課外讀物》第八冊，人民教育出版社

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Metadata

Work ID: 95041
Document ID: 262336
Title: 雉兔同籠
Corpus root: 維基大典
Page title: 雉兔同籠
File: 雉兔同籠.txt
Path: 維基大典/clean/雉兔同籠/雉兔同籠.txt

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雉兔同籠，又曰和尚分菓，可以二元一次方程算題也，出於孫子算經。原問問今有雉、兔同籠，上有三十五頭，下有九十四足。問：雉、兔各幾何？答雉二十三，兔一十二。術一：上置三十五頭，下置九十四足。半其足，得四十七，以少減多，再命之，上三除下三，上五除下五，下有一除上一，下有二除上二，即得。術二：上置頭，下置足，半其足，以頭除足，以足除頭，即得。此為砍足法，中外之首創也。凡例問百和尚，分饃百，大和尚每人著三，小和尚三人著一，問大小和尚各若干人? 答大和尚二十五人，小和尚七十五人。法大和尚一著三，小和尚三著一，相加即四和尚食生菓，以四除一百，得二十五為大和尚數，餘即小和尚數也。據簡明珠算陳湘記書局民國廿七年版孫子算經《數學課外讀物》第八冊，人民教育出版社