Geometry of coin-weighing problems

Noga Alon*, Dmitry N. Kozlov, Van H. Vu

*Corresponding author for this work

Research output: Contribution to journalConference articlepeer-review

Abstract

Given a set of m coins out of a collection of coins of k unknown distinct weights, we wish to decide if all the m given coins have the same weight or not using the minimum possible number of weighings in a regular balance beam. Let m(n, k) denote the maximum possible number of coins for which the above problem can be solved in n weighings. We show that m(n, 2) = n( 1/2 +o(l))n, whereas for all 3≤k≤n+1, m(n, k) is much smaller than m(n, 2) and satisfies m(n, k) = Θ(n log n/log k). The proofs have an interesting geometric flavour, and combine Linear Algebra techniques with geometric, probabilistic and combinatorial arguments.

Original languageEnglish
Pages (from-to)524-532
Number of pages9
JournalAnnual Symposium on Foundations of Computer Science - Proceedings
StatePublished - 1996
EventProceedings of the 1996 37th Annual Symposium on Foundations of Computer Science - Burlington, VT, USA
Duration: 14 Oct 199616 Oct 1996

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