منابع مشابه
The general counterfeit coin problem
Given c nickels among which there may be a counterfeit coin, which can only be told apart by its weight being di erent from the others, and moreover b balances. What is the minimal number of weighings to decide whether there is a counterfeit nickel, if so which one it is and whether it is heavier or lighter than a genuine nickel. We give an answer to this question for sequential and nonsequenti...
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In this discussion we examine two versions of the famous Counterfeit Coin Problem, focusing on their educational OR/MS content. It is shown that this problem provides an excellent environment for illustrating a number of fundamental OR/MS problem-solving concepts and methods related to decision making under uncertainty. A number of interactive modules are provided for experimentation with this ...
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Let Xm,ε be the distribution over m bits (X1, . . . , Xm) where the Xi are independent and each Xi equals 1 with probability (1 + ε)/2 and 0 with probability (1 − ε)/2. We consider the smallest value ε∗ of ε such that the distributions Xm,ε and Xm,0 can be distinguished with constant advantage by a function f : {0, 1}m → S which is the product of k functions f1, f2, . . . , fk on disjoint input...
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The number of partitions of n into parts divisible by a or b equals the number of partitions of n in which each part and each difference of two parts is expressible as a non-negative integer combination of a or b. This generalizes identities of MacMahon and Andrews. The analogous identities for three or more integers (in place of a, b) hold in certain cases.
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In the coin problem, one is given n independent flips of a coin that has bias β > 0 towards either Head or Tail. The goal is to decide which side the coin is biased towards, with high confidence. An optimal strategy for solving the coin problem is to apply the majority function on the n samples. This simple strategy works as long as β > Ω(1/ √ n). However, computing majority is an impossible ta...
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ژورنال
عنوان ژورنال: Scientific American
سال: 1919
ISSN: 0036-8733
DOI: 10.1038/scientificamerican04051919-220asupp