Optimal detection of two counterfeit coins with two-arms balance Original Research Article

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.