Puzzleup 2012 (1) Fifty Coins - 拼圖

題目網址: www.puzzleup.com/2012/puzzle/?240
加分時限: 7/26 7PM - 8/2 7PM

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）　　

◆Fifty Coins

There are 50 coins. Half of them are genuine and the other half are
counterfeit. Genuine coins weigh 10 grams, while counterfeit coins differ
from the genuine coins by 1 gram (some of them weigh 9 grams, and some of
them weigh 11 grams). You have a balance scale with two pans. In each
weighing the scale shows the difference of the weights placed in each pan.
You will randomly choose a coin. What is the minimum number of weighings
necessary to guarantee to determine whether it is genuine or not?

Notes:
*You can't use the chosen coin in the weighing processes.
*You must place at least one coin to each pan.
*The scale displays only the difference of the weights as a non-negative
number. It doesn't give any information that which side is heavier.

這裡有五十枚硬幣，有一半是真幣，一半是假幣。
真幣每個重十克，而假幣則和真幣差一克（有些是九克，有些是十一克）。
現在有個天平，每次秤時可以顯示兩個秤盤上的重量差。
若隨機選擇一個硬幣，問至少要秤幾次才能確定這幣是真幣還假幣？

註：
*你不能將所選的硬幣放上秤。
*每次上秤至少兩盤要各放一個硬幣。
*天平只會告訴你兩盤的重量差而不會說哪邊比較重。

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第一題就來這招啊...

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1985/01/12 三嶋鳴海 1989/02/22 優希堂悟 1990/02/22 冬川こころ 1993/07/05 小町
つぐみ 歡迎來到 1994/05/21 高江ミュウ 1997/03/24 守野いづみ 1997/03/24 伊野瀬
チサト 1998/06/18 守野くるみ 打越鋼太郎的 1999/10/19 楠田ゆに 2000/02/15 樋口遙
2002/12/17 八神ココ 2011/01/11 HAL18於朱倉岳墜機 ∞與∫的世界 2011/04/02 茜崎空
啟動 2012/05/21 第貮日蝕計畫預定 2017/05/01~07 LeMU崩壞 2019/04/01~07 某大學合宿

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