Consider the set A={1,2,3,…,2n}, n≥3 and let x∈ A be unknown element. For given natural number S we are allowed to ask whether x belongs to a subset B of A such that the sum of the elements of B equals S. We investigate for which S it is possible to find x using a nonadaptive search.
2000 Mathematics Subject Classification: 91A46, 91A35. We consider nonadaptive search problem for an unknown element x from the set A = {1, 2, 3, . . . , 2^n}, n ≥ 3. For fixed integer S the questions are of the form: Does x belong to a subset B of A, where the sum of the elements of B is equal to S? We wish to find all integers S for which nonadaptive search with n questions finds x. We continue our investigation from [4] and solve the last remaining case n = 2^k , k ≥ 2.
In this article we explore the so-called two-dimensional tree− search problem. We prove that for integers m of the form m = (2^(st) − 1)/(2^s − 1) the rectangles A(m, n) are all tight, no matter what n is. On the other hand, we prove that there exist infinitely many integers m for which there is an infinite number of n’s such that A(m, n) is loose. Furthermore, we determine the smallest loose rectangle as well as the smallest loose square (A(181, 181)). It is still undecided whether there exist...
Page 1