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How to find many counterfeit coins? (English) Zbl 0593.05002

Author’s abstract: ”We propose an algorithm for finding m defective coins, that uses at most \(\lceil \log_ 3\left( \begin{matrix} n\\ m\end{matrix} \right)\rceil +15m\) weighings on a balance scale, where n is the number of all coins.”
Reviewer: P.Reichensperger

MSC:

05A05 Permutations, words, matrices
68P10 Searching and sorting
Full Text: DOI

References:

[1] Bellman, R.: Dynamic Programming. Princeton: Princeton Univ. Press 1957 · Zbl 0077.13605
[2] Bellman, R., Glass, B.: On various versions of the defective coin problem. Inf. Control4, 119–131 (1961) · Zbl 0105.33403
[3] Cairns, S.S.: Balance scale sorting. Amer. Math. Mon.70, 136–143 (1963) · Zbl 0116.12404 · doi:10.2307/2312882
[4] Katona, G.O.H.: Combinatorial search problems. In: A Survey of Combinatorial Theory, edited by J.N. Srivastava, et al., pp. 285–308. Amsterdam: North Holland 1973
[5] Manvel, B.: Counterfeit coin problems. Math. Mag.50, 90–92 (1977) · Zbl 0353.05001 · doi:10.2307/2689732
[6] Mead, D.G.: The average number of weighings to locate a counterfeit coin. IEEE Trans. Inf. Theory25, 616–617 (1979) · Zbl 0414.05002 · doi:10.1109/TIT.1979.1056091
[7] Smith, C.A.B.: The counterfeit coin problem. Math. Gaz.31, 31–39 (1947) · doi:10.2307/3608991
[8] Tosic, R.: Two counterfeit coins. Discrete Math.46, 295–298 (1983) · Zbl 0518.05004 · doi:10.1016/0012-365X(83)90123-1
[9] Tosic, R.: Three counterfeit coins (to appear) · Zbl 0518.05004
[10] Tosic, R.: Four counterfeit coins. Rev. Res. Fac. Sci. Univ. Novi Sad14, 97–108 (1984) · Zbl 0562.90036
[11] Winkelmann, K.: An improved strategy for a counterfeit coin problem. IEEE Trans. Inf. Theory28 120–122 (1982) · Zbl 0472.05002 · doi:10.1109/TIT.1982.1056434
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