Optimal detection of two counterfeit coins with two-arms balance

AbstractWe consider the following coin-weighing problem: suppose among the given n coins there are two counterfeit coins, which are either heavier or lighter than other n−2 good coins, this is not known beforehand. The weighing device is a two-arms balance. Let NA(k) be the number of coins from which k weighings suffice to identify the two counterfeit coins by algorithm A and U(k)=max{n|n(n−1)⩽3k} be the information-theoretic upper bound of the number of coins then NA(k)⩽U(k). We establish a new method of reducing the above original problem to another identity problem of more simple configurations. It is proved that the information-theoretic upper bound U(k) are always achievable for all even integer k⩾1. For odd integer k⩾1, our general results can be used to approximate arbitrarily the information-theoretic upper bound. The ideas and techniques of this paper can be easily employed to settle other models of two counterfeit coins

A Model of the Information Seeking and Decision Making of Online Coin Buyers

Introduction. The Everyday Life Information Seeking approach suggests that much information behaviour takes place in non-work settings, for example in the pursuit of leisure activities such as hobbies. This study focuses on a community of collectors to examine how they gather information to decide whether to purchase an item for their collection when the target item has an ambiguous or deficient description. Method. Manual scanning of eBay and other online discussion board for coin buyers led to 187 postings indicating an attempt to reach a purchase decision, or to authenticate a purchased coin, through solicitation or posting of advice. Analysis. Postings were coded as to whether they dealt with 1. Ambiguous images in a listing, 2. Ambiguous statements in a listing, 3. Information missing from a listing, or 4. Sharing of other information (not restricted to a coin listing) that might possibly be used to make a purchase decision or authentication. Results. Using the example postings and the investigator\u27s earlier experiences, a model of coin buyer decision making was created, outlining the different paths and strategies that collectors may take when faced with uncertainties. Conclusion. The Internet facilitates access to both documentary reference material, as well as human information sources. The formation of virtual communities is made possibly, alongside existing face-to-face communities of hobbyists. Further studies of collectors could benefit from comparisons of information behaviour in both virtual and actual worlds