Fake coin problems using balance scales to identify one fake coin and its type among n coins (n > 2) were solved by Dyson in 1946. Dyson gave adaptive solutions with the minimum number of weighings where later weighings may be dependent on results of past weighings. In 2003 Born et al. gave non-adaptive solutions where all weighings are predetermined. Both solutions require the computation of a Dyson set, which is a list of placement of each coin for each weighing. The computation of a Dyson set requires substantial amount of time when n gets larger. We present a bounded partition approach to the fake coin problems without computing any Dyson set. Our approach uses bounded partition of coins recursively until the problem size may be small enough to use at most one weighing.

翻译：1946年，戴森利用天平从n枚硬币（n > 2）中识别一枚假币及其类型的假币问题给出了自适应解，其中后续称重可能依赖于先前称重结果，且所用称重次数最少。2003年，博恩等人给出了非自适应解，其中所有称重均为预先设定。两种解法均需计算一个戴森集，即每枚硬币在每次称重中放置位置的列表。当n增大时，戴森集的计算需耗费大量时间。我们提出一种无需计算戴森集的假币问题有界划分方法。该方法递归地对硬币进行有界划分，直至问题规模减小到最多只需一次称重。