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Further results for the counterfeit coin problems

Published online by Cambridge University Press:  24 October 2008

J. M. Hammersley
J. M. Hammersley
Affiliation:
Lectureship in the Design and Analysis of Scientific ExperimentUniversity of Oxford
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Extract

The counterfeit coin problems consist in detecting and locating the anomalous weights of counterfeit coins amongst a set of genuine coins. Suppose that altogether there are n coins, of which at least n − k are known to be genuine. We do not know which coins are genuine; but we do know that all genuine coins have the same (unknown) weight. The weights of the remaining k coins are unspecified and possibly all different.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 46 , Issue 2 , April 1950 , pp. 226 - 230
Copyright
Copyright © Cambridge Philosophical Society 1950

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References

† Smith, C. A. B., ‘The counterfeit coin problem’, Math. Gaz. 31 (1947), 31–9.CrossRefGoogle Scholar

‡ Hammersley, J. M., ‘A geometrical illustration of a principle of experimental directives’, Phil. Mag. (7), 39 (1948), 460–6.CrossRefGoogle Scholar

† See, for example, Mood, A. M., ‘On Hotelling's weighing problem’, Ann. Math. Statist. 17 (1946), 432–46CrossRefGoogle Scholar, and Plackett, R. L. and Burman, J. P., ‘The design of optimum multifactorial experiments’, Biometrika, 33 (1946), 305–25CrossRefGoogle Scholar. These papers contain references to further material on the subject.