7 research outputs found
Coins of Three Different Weights
We discuss several coin-weighing problems in which coins are known to be of
three different weights and only a balance scale can be used. We start with the
task of sorting coins when the pans of the scale can fit only one coin. We
prove that the optimal number of weighings for coins is . When the pans have an unlimited capacity, we can sort the coins in
weighings. We also discuss variations of this problem, when there is exactly
one coin of the middle weight.Comment: 18 page
Minimum average-case queries of q + 1 -ary search game with small sets
Given a search space S={1,2,...,n}, an unknown element x*∈S and fixed integers ℓ≥1 and q≥1, a q+1-ary ℓ-restricted query is of the following form: which one of the set {A 0,A 1,...,A q} is the x* in?, where (A 0,A 1,...,A q) is a partition of S and | Ai|≤ℓ for i=1,2,...,q. The problem of finding x* from S with q+1-ary size-restricted queries is called as a q+1-ary search game with small sets. In this paper, we consider sequential algorithms for the above problem, and establish the minimum number of average-case sequential queries when x* satisfies the uniform distribution on S. © 2011 Elsevier B.V. All rights reserved