Detecting the two complementary defectives with a balance scale |
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Authors: | C. Christen F.K. Hwang |
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Affiliation: | Univercité de Montreal , Montréal, H3C3J7, Canada |
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Abstract: | We consider the problem of finding a pair of irregular boxes from a set of n boxes using a balance scale. One irregular box is heavier and the other lighter than a regular box but the total weight of the two irregular boxes is the same as the total weight of two regular boxes. Let N(w) denote the maximum number of boxes w weighings can handle. We give a weighing scheme such that N(2t) ≥3t for t ≥2 and N(2t + 1) ≥ 5.3t-1 for t ≥ 1. The N(2t) result meets the information-theoretic bound and hence is the best possible. |
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Keywords: | counterfeit coins weighing problems balance scale defectives detection schemes |
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