  We derive the exact ground-state energy of the one-dimensional Ising model in
random fields taking values h, 0 and -h with general probabilities. The
random-field Ising model on a ladder is also analyzed by showing its
equivalence to the random-field Ising chain with field values h, -h and 0 for
h<J. The zero-temperature transger matrix is used to obtain the results.
