Puzzleup 2018 (12) THE TELEPHONE GAME - 拼圖

題目網址: http://www.puzzleup.com/2018/
http://www.puzzleup.com/2018/puzzle/?12
答題時限: １０月18日７ＰＭ－比賽結束（約12月12日）
加分時限: １０月18日７ＰＭ－１０月24日６：５９ＰＭ

答對可得基本分１００分。答案可上傳５次，每改１次答案從基本分扣２０分。
比賽期間內可隨時上傳答案，加分時限內答對第ｎ天加（６－ｎ）分　 　　 　
另依題目的難易有額外加分（如有８０％的人這題答錯，答對者加８０分）　　

◆THE TELEPHONE GAME

2 people sit on a round table to play a variation of the telephone game.
They are numbered from 1 to 12 in clockwise order, i.e. the people with
adjacent numbers (including 1 and 12) sit next to each other. Person #1
chooses a secret word and starts the game by randomly selecting one of
the two neighbors and whispering the word to that person. Upon hearing
the word, each person continues the game by randomly selecting one of
the neighbors and whispering the word. The game ends when everyone knows
the secret word.

What is the probability that the last person whispering the word is
numbered 6?

Enter your answer as a reduced fraction. Example: 123/4567

12個人繞著圓桌坐著，開始玩一種變形的傳話遊戲。玩家們依順時鐘方向編號成
1至12號，號碼相鄰(包括1號與12號)的玩家座位相鄰。遊戲開始由1號玩家想出一
個密語，然後隨機從其兩位鄰居中挑選一位，將密語悄稍地告知那個人。每個人
聽到密語後，一樣隨機從其兩位鄰居中挑選一位，並悄稍告知密語。遊戲會在每
位玩家都知道密語後結束。

問最後一個傳達密語的玩家為6號玩家之機率？

以最簡分數回答，如 123/4567。

譯註：原文寫2 people，看題意應該為12 people。

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