  A permutiple is a number which is an integer multiple of some permutation of
its digits. A well-known example is 9801 since it is an integer multiple of its
reversal, 1089. In this paper, we consider the permutiple problem in an
entirely different setting: continued fractions. We pose the question of when
the simple continued fraction representation of a rational number is an integer
multiple of a permutation of its partial quotients (or digits, as we shall call
them). We develop some general results and apply them to finding new examples.
In doing so, we attempt to classify all 2, 3, and 4-digit continued fraction
permutiples in terms of basic permutiple types which we discover along the way.
We also generate new examples from old by finding conditions which guarantee
that digit-string concatenation yields other permutiples.
