【摘要】 考虑两伪币的搜索问题:给定外观相同的n个硬币,其中有两个比较重的伪币,通过等臂天平在尽可能少的称量次数下去找出两个伪币.L^（2）（n）为最坏情况下找到两伪币的最小称量步数.对于任意的n≥2,满足log₃（₂ⁿ）]≤L^（2）（n）≤[log₃（₂ⁿ）]+1.猜想信息理论下界均可达.通过一个新的方法扩大了满足信息理论下界的n的取值范围.更多还原

【Abstract】 The following weighting problem is considered:determine two counterfeit coins which are heavier than good coins in a set of n coins of the same appearance using only an equal arms balance.Let L^（2）（n） denote the minimum number of weighings necessary when exactly two of n coins are known to be defective.For all n ≥ 2,it satisfies[log₃（₂ⁿ）]≤L^（2）（n） ≤[log₃（₂ⁿ）1 + 1.It was conjectured that the lower bound is always achieved.In this paper,using a novel algorithm,we improve on the range of n for which the lower bound is reached.更多还原