1. A method for compulsory participation of weighing machines in a combinatorial weighing system having a control apparatus which includes a processor for performing combinatorial computations based on weight values produced as outputs by respective ones of a plurality of weighing machines for weighing or counting articles supplied thereto, and a data memory having storage areas corresponding to respective weighing machines, the control apparatus performing the combinatorial computations to compute combinations of the weight values produced by the weighing machines, selecting a single combination the total weight of which falls within preset allowable limits, discharging the articles from the weighing machines belonging to the single combination selected, and compelling a predetermined weighing machine to participate in the combinatorial computations, said method being performed under the control of the control apparatus and comprising the steps of: (a) updating, by a predetermined amount, data stored in the storage areas of the data memory whenever a single combination within the preset allowable limits is selected by a combinatorial computation, the updated storage areas corresponding to the weighing machines not selected as part of the selected single combination; (b) resetting data stored in the storage areas of the data memory whenever a single combination within the preset allowable limits is selected by a combinatorial computation, the reset storage areas corresponding to the weighing machines which are selected as part of the selected single combination; (c) determining whether the data in each of the storage areas of the data memory is indicative of a value less than a first set threshold value, equal to or greater than the first set threshold value and less than a second set threshold value, or equal to or greater than the second set threshold value; (d) obtaining, when the data stored in all of the storage areas of the data memory are indicative of values less than the first set threshold value and from among all combinations of all weighing machines, a combination of weighing machines giving a total weight value equal to a target value or closest to the target value within the preset allowable limits; (e) compelling, when the data stored in all of the storage areas of the data memory are indicative of values less than the second set threshold value and the data stored in at least one storage area is indicative of a value equal to or greater than the first set threshold value, the weighing machine corresponding to the at least one storage area to participate in the combinatorial computations; (f) obtaining, solely from among combinations that contain the weighing machine compelled to participate in the combinatorial computations in said step (e), a combination of weighing machines giving a total weight value equal to the target value or closest to the target value within the preset allowable limits; (g) compelling, when the data stored in at least one of the storage areas of the data memory is indicative of a value equal to or greater than the second set threshold value, the weighing machine corresponding to the at least one storage area to participate in the combinatorial computations, and raising an upper limit value of the preset allowable limits to obtain adjusted preset allowable limits; (h) obtaining, solely from among combinations that contain the weighing machine compelled to participate in the combinatorial computations in said step (g), a combination of weighing machines giving a total weight value equal to the target value or closest to the target value within the adjusted preset allowable limits; and (i) discharging the articles from the combination of weighing machines obtained in said steps (d), (f), or (h).