American Mathematical Monthly
Combinatorial search
On the conjecture at two counterfeit coins
Discrete Mathematics
Optimal detection of a counterfeit coin with multi-arms balances
Discrete Applied Mathematics
A predetermined algorithm for detecting a counterfeit coin with a mutli-arms balance
Discrete Applied Mathematics
Searching for two counterfeit coins with two-arms balance
Discrete Applied Mathematics
Minimal average cost of searching for a counterfeit coin: restricted model
Discrete Applied Mathematics
Searching for a counterfeit coin with b-balance
Discrete Applied Mathematics
Searching for a counterfeit coin with two unreliable weighings
Discrete Applied Mathematics - Special issue: Max-algebra
Searching for two counterfeit coins with two-arms balance
Discrete Applied Mathematics
Searching for a counterfeit coin with two unreliable weighings
Discrete Applied Mathematics
Minimum average-case queries of q+1-ary search game with small sets
Discrete Applied Mathematics
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We consider the following coin-weighing problem: suppose among the given n coins there are two counterfeit coins, which are either heavier or lighter than other n - 2 good coins, this is not known beforehand. The weighing device is a two-arms balance. Let NA(k) be the number of coins from which k weighings suffice to identify the two counterfeit coins by algorithm A and U(k)=max{n | n(n - 1) ≤ 3k} be the information-theoretic upper bound of the number of coins then NA(k) ≤ U(k). We establish a new method of reducing the above original problem to another identity problem of more simple configurations. It is proved that the information-theoretic upper bound U(k) are always achievable for all even integer k ≥ 1. For odd integer k ≥ 1, our general results can be used to approximate arbitrarily the information-theoretic upper bound. The ideas and techniques of this paper can be easily employed to settle other models of two counterfeit coins.