Puzzleup 2018 (10) SCALE - 拼圖

題目網址: http://www.puzzleup.com/2018/
http://www.puzzleup.com/2018/puzzle/?10
答題時限: １０月4日７ＰＭ－比賽結束（約12月12日）
加分時限: １０月4日７ＰＭ－１０月10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）　　

◆SCALE

There are X balls that look identical. All balls except one has the same
weight. The different ball is either lighter or heavier than the others.

You have a balance scale with two plates and you can only use it to compare
the weights of the balls. With each use you can put any number of balls in
each plate and as a result find out which side is heavier or if the two
sides have the same weight.

You can guarantee finding the different ball and whether it is lighter
or heavier by using the scale at most 4 times. What is the maximum possible
X satisfying this condition?

有X顆外觀一樣的球。每顆球具有相同的重量，除了其中一顆。該顆球或許比其它
球重，或是較輕。

你有一個天秤，帶兩個底座，只可用來比較球的重量。每次使用時，你在各底座上
放置任意數量的球，並可得到哪邊較重或是一樣重的結果。

在至多使用天秤四次的情形下，你能保證可以找出重量不一樣的球，且能知道該顆
球是較輕或較重的。問能滿足上述前提之最大可能X值？


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