Ratchet writing is a method of writing information into certain nondestructive-readout (NDRO) magnetic memory elements. Writing is accomplished by reversing (or "ratcheting") the flux about one hole of the element with a word-oriented wire while simultaneously applying information-determined bit current to another hole called the storage hole. The effect of ratcheting is a threshold reduction for switching about the storage hole. It is established that ratchet writing is possible because some of the flux switched by the ratchet current closes by returning around the storage hole rather than through the "common volume" between the two holes. The detailed switching properties of a simple thin-wall core are computed and compared with experiment. The results are in excellent agreement within the limitations of the approximations made. It is found that there is a region where the bit-current threshold declines linearly with unit slope as ratchet current is increased. In this region there is a direct transfer of flux from the ratcheted hole to the storage hole, the common volume remaining an open circuit.