  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.
