解救村民
從前有個皇帝，有一天他心情不好，決定拿他統治下的其中一條村的人出氣。他要與這整條村的村民玩一個遊戲︰<br>
全村一百人要向前排一直線，每個村民頭上被套上一隻帽子，帽子只有黑色或白色，而被套上帽的村民不知自己所戴的帽是什麼顏色。由排在最後的一人開始，每人要猜自己的帽的顏色，猜對的即時放走，猜錯的即時殺掉。<br>
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當然，皇帝為了防止作弊，規定遊戲時村民只能叫出自己猜的顏色「黑」或「白」，多說其他字或發出任何其他聲音或做其他動作都算作弊，全村一百人一律殺掉。當然偷看自己的帽也會被殺。<br>
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收到這消息，村民只好向路過的智者(即係你)求助。你會教村民如何做，才可確保最多的生還人數呢？(即保証一定數量的村民猜中自己的帽的顏色)<br>
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注意︰<br>
- 排隊的村民可以看見自己前面的所有人所戴的帽的顏色(即排第二的可看見排第一個的；排最後的可看見前面99人的)<br>
- 所有村民可以聽到自己背後的村民猜什麼，亦即時知道他是否猜對<br>
- 所有村民都相親相愛，甚至願意為其他村民犧牲<br>
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<font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">可確保</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">50</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">人生還的方法</font></font></font></font><font face="Arial "><font size="1"><br>
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<font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">方法很簡單，教村民於排隊之後，最後一人直接說出他前面那人的帽子的顏色，第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">99</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">人聽到就知道自己帽子的顏色；第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">98</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">人說出第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">97</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">人的帽子的顏色，如此類推，即所有排單數的村民</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">(</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">1</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">個、第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">3</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">個……第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">99</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">個</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">)</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">都可以聽身後的人所喊出的顏色得知自己帽子的顏色，從而確保猜對自己的顏色得以保性命。至於排雙數的村民</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">(</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">2</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">個、第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">4</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">個……第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">100</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">個</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">)</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">只好聽天由命，若他帽子的顏色剛好與面前的相同，那便可以活命了。所以說這方法最少有一半人是確保不用被殺。</font></font></font></font><font face="Arial "><font size="1"><br>
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<font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">太簡單了？其實還有方法可以救更多的人喔！大家再想想看!</font></font></font></font><br>
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<font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">答案︰</font></font></font></font><font face="Arial "><font size="1"><br>
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<font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">可以確保</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">66</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">人性命的方法。</font></font></font></font><font face="Arial "><font size="1"><br>
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<font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">其實方法並不複雜，就是以</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">3</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">人為一組，最後一人以顏色為代表報出面前兩人帽子的顏色是否相同。以最後三人為例，先約定「黑」表示相同；「白」表示不同；當第</font></font></font></font><font face="Arial "><font size="1"><font face="Arial "><font style="font-size: 9pt">100</font></font></font></font><font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">個村民，看見前面兩人(第99和第98)的帽子，如果顏色相同，他便喊「黑」；不同便喊「白」，第99人聽到，再看見面前第98人的帽的顏色，便可以確認自己的顏色；第98人聽到第100人和第99人的答案，亦可以得知自己的顏色。所以每3人便有2人可以確保安全，其餘的34人則各安天命了~</font></font></font></font><br>
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<font face="PMingLiU "><font size="1"><font face="PMingLiU "><font style="font-size: 9pt">三分二的確保生還率，功德無量？作為真正智者的你，又豈會甘於只能拯救66人？當然還有方法救更多的村民，來，各位不要吝惜你們的智慧，想個方法救救村民吧！答案將於星期五晚公報。(還是往下拉吧)</font></font></font></font><br>
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<font face="新細明體 ">無錯！就是可以確保救99人！</font><br><br><font color="Blue" size="4">答案分享︰</font><br>
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