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doi:10.1016/0097-3165(90)90072-5 
Copyright © 1990 Published by Elsevier Inc.
How many random questions are necessary to identify n distinct objects?
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B. Pittel and H. Rubin
Received 15 August 1987.
Communicated by the Managing Editors
Available online 20 July 2004.
Abstract
Suppose that X and A are two finite sets of the same cardinality n 
2. Assume that there is a bijective mapping φ: X → A which is unknown to us, and we must determine it. We are allowed to ask a sequence of questions each posed as follows. For a given B 
A what is φ−1(B)? In this paper we study a case when the subsets B are chosen uniformly at random. The main result is: if each subset has to split all the atoms of a field generated by the previous subsets, then the total number of questions (needed to determine the mapping completely) is log2 n + (1 + op(1))(2 log2 n)1/2. Here op(1) stands for a random term approaching 0 in probability as n → ∞.
