Abstract
We propose an algorithm for findingm defective coins, that uses at most\(\left\lceil {\log _3 \left( {\begin{array}{*{20}c} n \\ m \\ \end{array} } \right)} \right\rceil \) + 15m weighings on a balance scale, wheren is the number of all coins.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Bellman, R.: Dynamic Programming. Princeton: Princeton Univ. Press 1957
Bellman, R., Glass, B.: On various versions of the defective coin problem. Inf. Control4, 119–131 (1961)
Cairns, S.S.: Balance scale sorting. Amer. Math. Mon.70, 136–143 (1963)
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
Manvel, B.: Counterfeit coin problems. Math. Mag.50, 90–92 (1977)
Mead, D.G.: The average number of weighings to locate a counterfeit coin. IEEE Trans. Inf. Theory25, 616–617 (1979)
Smith, C.A.B.: The counterfeit coin problem. Math. Gaz.31, 31–39 (1947)
Tosic, R.: Two counterfeit coins. Discrete Math.46, 295–298 (1983)
Tosic, R.: Three counterfeit coins (to appear)
Tosic, R.: Four counterfeit coins. Rev. Res. Fac. Sci. Univ. Novi Sad14, 97–108 (1984)
Winkelmann, K.: An improved strategy for a counterfeit coin problem. IEEE Trans. Inf. Theory28 120–122 (1982)
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Pyber, L. How to find many counterfeit coins?. Graphs and Combinatorics 2, 173–177 (1986). https://doi.org/10.1007/BF01788090
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01788090