Rats and Poisoned water
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1 of 1000 bottles of water is poisoned which will kill a rat in 1 week if the rat drunk any amout of the water. Given the bottles of water have no visual difference, how many rats are needed at least to find the poisoned one in 1 week?
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本题主要考察二进制与十进制的转换,但更多的需要灵活的思考问题。1000瓶水里只有一瓶有毒,但具体是哪一瓶未知,将这1000瓶水按二进制的方式编号1-1000,即0000000001、0000000010、0000000011、……、1111100111,然后小白鼠10只分别按顺序排列,即小白鼠喝与不喝某瓶水用0和1表示,所以10只小白鼠共能表示1024(210)种状态,1000瓶水按编号来喂小白鼠(如编号为1000110101时,给小白鼠1、3、5、6、10喂水),一周后观察结果,若1、3、5、6、10这几只小白鼠死亡,则代表编号为1000110101的瓶子中的水有毒,同理若1、2、3这三只小白鼠死亡,则代表编号为000000111的水有毒。
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