組合分析 - 多少個小貓咪咪？(revised 1.0)

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在英國有好幾個地方叫 St. Ives 的，這張是其中的一個博物館頂樓照的。 （點擊圖片見更多信息）

   當塞翁被喚作塞青還是在念博士課程的時候，要選四門功課作為獲取博士候選生資格的考核課題，並分別在連續的四天內，至少通過其中的兩門否則全部作廢。塞青所選課題，包含一門基礎概率，用的是南加大 Sheldon Ross 教授的 《A First Course In Probability》；憑著中學微薄的一點高等數學基礎，挑燈夜戰，勉強過關。

   記得 Ross 教授在第一章中給出的一道組合習題很簡單，用不著組合概念，也很有意思；它要求從一首童謠 (nursery rhyme) 講的故事，計算出有多少個小貓咪咪。塞翁把那本書找出來了，將那首童謠的開始部分抄錄如下，並想看看大家能否在念完童謠之後的半分鍾之內將答案或算法列出來。不過注意了，盡管叫作童謠，還是不適合念給家裏小朋友的噢...：
  
   As I was going to St. Ives 
   I met a man with 7 wives.
   Each wife had 7 sacks.
   Each sack had 7 cats.
   Each cat had 7 kittens.
   How many kittens did the traveler meet?

   好了，念完了吧？

   別忘了要 post your solution here... 
   
   Bye-bye... and see you next time!

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A little more on St. Ives, and listen for the words that'd be pleasing the ear...(點擊此處，and listen for English's English.)

There are two other versions of the nursery rhyme in publications...

The first version:

As I was going to St Ives

I met a man with seven wives

         And every wife had seven sacks
         And every sack had seven cats
         And every cat had seven kits

         Kits, cats, sacks, wives
         How many were going to St Ives?

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The second version:

As I was going to St Ives

I met a man with seven wives

Seven wives with seven sacks

Seven sacks with seven cats

Seven cats with seven kits

Kits, cats, sacks, wives

How many were going to St Ives?


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