Counting method

A counting method comprising the steps of weighing a number of articles dividedly by n weighing machines, dividing the weights measured by the weighing machines by the unit weight of the articles to find the respective numbers of articles in the weighing machines, calculating combinations of these numbers to find the combination numbers associated with the respective combinations, finding a particular combination whose combination number is equal or closest to a set number, and discharging the groups of articles corresonding to the particular combination from the corresponding weighing machines, while calculating a new unit weight from a weight or weights measured by one or a plurality of the weighing machines and from the number or numbers of articles in this one or plurality of the weighing machines, such new unit weight being used for the next calculation of numbers.

The present invention relates to a method of counting articles with 
increased accuracy in combinatorial counting of articles which have 
variations in the weight of a single article (hereinafter referred to as 
unit weight), such as packaged cups of bolts, nuts, and milk. 
In the case of combinatorial counting which comprises the steps of weighing 
groups of articles respectively by a plurality of weighing machines, 
converting the weight measured by each weighing machine into the number of 
articles in each group, and performing combinatorial calculations of the 
individual weights to obtain a predetermined number of articles, said 
conversion of weights into numbers is performed by dividing each measured 
weight by the unit weight, or the weight of a single article. However, if 
there is an error in the unit weight, this results in an error in the 
number of articles calculated for each weighing machine and hence an error 
in the combination number obtained by performing combinatorial 
calculations, thus making accurate counting impossible. Further, the 
greater the number of articles weighed by a single weighing machine, the 
greater the error in the calculated number. Therefore, in order to 
calculate the number of articles accurately, it is necessary to find the 
unit weight accurately. However, since articles vary in the unit weight, 
as described above, it would be nonsense to weigh a single article 
accurately for the purpose of finding the unit weight. Thus, it would be 
better to find the unit weight by weighing a number of articles and 
dividing their weight by the number of articles; the greater the number of 
articles to be weighed, the more accurately can the unit weight be 
ontained. Therefore, it is preferable that the value for the unit weight 
of articles which is determined by suitable means at the start of weighing 
operation be replaced by a new value obtained by calculation in each 
weighing operation. In order to find the unit weight more accurately, 
there is a method of renewing the unit weight for each weighing operation, 
which comprises the steps of initially charging each weighing machine with 
a lesser number of articles and gradually increasing the number of 
articles to be charged into each weighing machine in successive weighing 
operations until it corresponds to the number of articles to be obtained. 
Further, where combinatorial counting is repeated, there are cases where 
the unit weight of articles gradually decreases (or increases) as a whole 
with the lapse of time. This occurs, e.g., when milk is charged into cups, 
because the viscosity of milk varies with ambient temperature. In this 
case also, it is necessary to calculate the unit weight of articles for 
renewal in each weighing operation. 
Accordingly, it is an object of the present invention to provide more 
accurate combinatorial counting by calculating the unit weight from the 
weight or weights of articles weighed by a single or a plurality of 
weighing machines in each combinatorial operation, to renew the value for 
the unit weight so as to obtain a more accurate value for the unit weight. 
According to the invention, since the unit weight for calculating the 
number of articles from their weight can be obtained from the weight of a 
number of articles which is actually calculated, the counting accuracy can 
be increased. According to the invention, even if the unit weight of 
articles gradually varies during counting, such variations can be 
automatically accommodated by renewing the unit weight of articles in each 
counting operation, so that very accurate counting can be effected. 
Further, according to the invention, since the unit weight is 
automatically renewed by weighed articles themselves through combinatorial 
weighing, the initial setting of unit weight can be very accurately 
effected, even in the case of weighing a large number of articles, by 
initially weighing a relatively small number of articles and then 
gradually increasing the number of articles to be weighed. 
A combinatorial counting method has heretofore been known, comprising the 
steps of charging a plurality of weighing machines each with a number of 
articles with suitable variations, dividing the weight value of articles 
obtained by each weighing machine by the unit weight of articles to find 
the number of articles, calculating combinations of the weights to find a 
particular combination which is equal or closest to a set number, and 
discharging the articles from the weighing machines corresponding to said 
particular combination. Thus, in this counting method, if the unit weight 
of articles for finding the number of articles from the weighed value of 
the articles is fixed at the initially set value, there is a possibility 
that the error in this set unit weight increases with respect to the unit 
weight of the articles which are to be actually weighed. This is because 
the value used for initially setting the unit weight of articles is either 
a value obtained by weighing usually a single or several articles by a 
separate weighing machine or a value which is preset as the standard 
weight of such article. Since the unit weight of articles will differ from 
article to article or vary with such factors as the conditions of the 
machine used for producing such articles and the quality of the material 
of the articles, even if efforts are being made to keep the unit weight of 
articles at a fixed value, the unit weight will vary with the lapse of 
time. Therefore, it is more preferable that the unit weight used in said 
combinatorial counting be obtained from the weighed value of a number of 
articles being actually weighed, by dividing said value by the number of 
articles. 
With the above in mind, the present invention provides improvements. More 
particularly, the invention consists in weighing a large number of 
articles by n weighing machines, dividing the weight measured by each 
weighing machine by the unit weight to find the number of articles 
contained in each weighing machine, calculating combinations of the 
individual numbers to find a particular combination which is equal or 
closest to a set weight, while calculating a new unit weight from the 
weight or weights measured by one or a plurality of said weighing machines 
and from the number or numbers of articles contained in said weighing 
machine or machines, and using this new unit weight for the next 
calculation of numbers. 
The invention has many embodiments as to the method of finding a new unit 
weight after combinatorial counting. These embodiments will be suitably 
selectively used singly or in combinations, depending upon the kind of 
articles to be counted or upon the purpose of counting. 
Thus, in a counting method comprising the steps of dividing the weighed 
values of articles obtained by a plurality of weighing machines by the 
unit weight to find the numbers, and calculating combinations of these 
numbers to find a particular combination equal or closest to a set number, 
the invention consists in dividing the weighed value of the actually 
weighed articles by the number of said articles to find the unit weight, 
the latter being then used as a new unit weight for the next combinatorial 
counting, so that combinatorial counting can be performed with very high 
accuracy. Further, even if the average unit weight of articles gradually 
varies during repeated combinatorial counting, this is automatically 
compensated to allow combinatorial counting to be effected with the proper 
unit weight at all times.

In FIG. 1 showing a combinatorial counting apparatus according to the 
present invention using a microcomputer, 1.sub.1 . . . 1.sub.n denote n 
weighing machines for weighing articles, and 2 denote a multiplexer for 
successively transferring analog weight voltages produced by the weighing 
machines 1.sub.1 . . . 1.sub.n in response to selection signals to be 
later described, said multiplexer being composed, e.g., of analog 
switches. The numeral 3 denotes an A/D converter for converting analog 
weight voltages from the multiplexer 2 into digital weight signals; 4 
denotes an arithmetic control section composed of a microcomputer or the 
like; 5 denotes a unit weight setting section for setting the unit weight 
of articles; 6 denotes a number setting section for setting the number of 
articles to be counted; 7 denotes a weight setting section for setting the 
total weight of that number of articles which has been set by the number 
setting section 6; 8 denotes an upper weight limit setting section for 
setting the upper limit weight for the total weight of a set number of 
articles; and 9 denotes a lower weight limit setting section for setting 
the lower weight limit. FIG. 2 is a flowchart showing an example of the 
operation of the arithmetic control section 4, which will now be 
described. 
The n weighing machines 1.sub.1 . . . 1.sub.n have been charged each with a 
division of a number of articles. When a start signal a from a packaging 
machine (not shown) for packaging counted articles is transferred to the 
arithmetic control section 4, the latter transfers a selection signal b to 
the multiplexer 2. In response to the selection signal, the multiplexer 2 
transfers the analog weight voltages, which have been transferred thereto 
from the weighing machine 1.sub.1 . . . 1.sub.n, successively to the A/D 
converter 3, and the A/D converted weights are stored in the arithmetic 
control section 4. The arithmetic control section 4 divides each weight 
stored therein by the unit weight set by the unit weight setting section 5 
and rounds the quotient to the nearest integer, thus converting the 
weights of the articles in the weighing machines 1.sub.1 . . . 1.sub.n 
into the respective numbers of articles therein and storing said numbers. 
The arithmetic control section 4 adds the stored numbers of articles in 
the weighing machines 1.sub.1 . . . 1.sub.n in accordance with all of the 
combination codes indicating the combinations of the weighing machines to 
calculate combination numbers for the combination codes, stores these 
combination numbers and combination codes in pairs, and compares the set 
number set by the number setting section 6 with all of the stored 
combination numbers to search for a combination code which agrees in 
number, and stores it. However, if there is no combination which agrees in 
number, it judges that counting is impossible, and turns on a warning 
lamp, for example, moving to a suitable error processing treatment. 
Further, the arithmetic control section 4 adds the weights of the articles 
in the weighing machines 1.sub.1 . . . 1.sub.n in accordance with the 
combination numbers which are equal to the set number of calculate the 
combination weights and searches for a combination of weights, among these 
combination weights, which is equal or closest to the set weight set by 
the weight setting section 7 and stores such combination weight and 
combination code as a pair. It compares this stored combination weight 
with the upper weight limit set by the upper weight limit setting section 
8 and the lower weight limit set by the lower weight limit setting section 
9, and if this combination weight is not between the upper and lower 
weight limits, it judges that counting is impossible, and turns on a 
warning lamp, for example, moving to a suitable error processing 
treatment. If said combination weight lies between the upper and lower 
weight limits, the arithmetic control section 4 transfers discharge 
signals in accordance with the combination code associated with said 
combination weight. The articles in the weighing machines corresponding to 
the discharge signals are discharged, so that articles whose number is 
equal to the set number are fed to the packaging machine. At this time, 
the arithmetic control section 4 calculates a new unit weight from the 
weight or weights of the articles in a desired one or more of the weighing 
machines and the number or numbers of articles therein and stores said new 
unit weight. The new unit weight is used when the numbers of articles are 
calculated from the weights of the articles in the weighing machines 
1.sub.1 . . . 1.sub.n in the next counting. In addition, there are various 
methods of finding this new unit weight, which will be later described in 
block. 
Thereafter, the next counting operation will be performed in the same 
manner as described above. 
First, the weighing machines from which articles have been discharged are 
fed with fresh articles and when a start signal a is transferred to the 
arithmetic control section 4, the weights of articles in the weighing 
machines 1.sub.1 . . . 1.sub.n are stored in the same manner as in the 
preceding case. These weights are divided by the new unit weight which was 
calculated in the preceding counting and stored, the quotients being 
rounded to the nearest integers, whereby the weights of the articles in 
the weighing machines 1.sub.1 . . . 1.sub.n are converted to the numbers 
of articles. As in the preceding case, a combination whose combination 
number is equal to the set number and whose combination weight lies 
between the upper and lower weight limits and equal or closest to the set 
weight is searched for. If a combination which satisfies these conditions 
is obtained, discharge signals are transferred from the arithmetic control 
section in accordance with this combination. In this case also, this 
combination weight which has been discharged is divided by the set weight 
to calculate a new unit weight, which is stored in place of the new unit 
weight which was calculated and stored in the preceding counting operation 
and is used for the next counting operation. Thereafter, the same 
procedure is followed and the unit weight is renewed for each counting 
operation. 
As described above, the invention consists in calculating the number of 
articles in each weighing machine by a preset unit weight for the first 
combinatorial counting, and calculating and storing a new unit weight for 
the next combinatorial counting, so that in and after the second 
combinatorial counting, the number of articles in each weighing machine is 
calculated by the new unit weight calculated and stored during the 
preceding counting and the new unit weight is renewed for the next 
counting. 
Some concrete methods of finding new unit weights in the above arrangement 
will now be described. 
A first method of finding new unit weights is characterized in that when 
discharged signals are transferred from the arithmetic control section 4 
after combinatorial calculations in accordance with the result of said 
combinatorial calculations, the arithmethic control section 4 calculates a 
new unit weight by dividing the weight of the discharged articles, i.e., 
the combination weight which is equal or closest to the set weight, by the 
number of discharged articles, i.e., the set number, said new unit weight 
being stored in the arithmethic control section 4 for use in the next 
combinatorial calculation. 
A second method of finding new unit weights is characterized in that the 
combination weights in those combinations whose combination numbers are 
equal to the set number are rearranged in decreasing or increasing order, 
and one combination weight which is at the middle of the series (i.e., 
median) is divided by that combination number to find a new unit weight. 
The usefulness of this second method will now be described. In the case 
where the first method is used, if, for example, there are 5 combinations 
whose combination numbers are equal to the set number and whose 
combination weights are 199 g, 200 g, 196 g, 197 g, and 194 g, and the set 
number is 200 g, then the combination whose combination weight is 200 g 
will be discharged and a new unit weight will be calculated by dividing 
this combination weight 200 g by the combination number. However, where 
combination weights are distributed more predominantly in the 
smaller-value region (or larger-value region) with respect to the set 
weight, as in this case, a new unit weight can be found more accurately by 
dividing the combination weight which lies in the middle of the 
combination weight series (median) (in the above example, 197 g) by the 
combination number than by dividing the combination weight which is equal 
or closest to the set weight by the combination number. 
In the first and second methods, a new unit weight is calculated from the 
combination weight in one combination and the combination number in that 
combination. However, it is possible to calculate a new unit weight from 
the combination weights in a plurality of combinations and the combination 
numbers in those combinations and to store said new unit weight. This will 
now be described as third through sixth methods. 
The third method of finding new unit weights comprises the steps of 
dividing the combination weights in all or any of those combinations whose 
combination numbers are equal to the set number respectively by said 
combination number to find unit weights, calculating the average of these 
unit weights, and storing said average as a new unit weight. 
The usefulness of this third method will now be described. Where a 
plurality of combinations whose combination numbers are equal to the set 
number are obtained, a combination whose total weight is closest to the 
set total weight to be discharged is selected from the combinations and 
the articles are discharged from the corresponding weighing machines. In 
this case, if a new unit weight is obtained by dividing the total weight 
of the discharged combination by the set number, errors will become 
greater when the unit weight is varying. That is, where the unit weight is 
varying, the total weight in each combination is also varying in the same 
direction as the unit weight as a whole. In this case, it is better to 
adopt a way of finding new unit weights which reflects the value of the 
varying total weight. Therefore, although what is discharged is the 
combination closest to the set total weight, a new unit weight is found by 
calculating a unit weight for each of the combinations which are equal to 
the set number and calculating the average of these unit weights, the new 
unit weight thus found being close to the average of the actual unit 
weights, which minimizes the probability of errors in individual 
calculations. 
The fourth method of finding new unit weights will be described. First, the 
upper and lower limits of the number of articles are provided. Of the 
calculated and stored combinations and their combination numbers, all or 
any of those combinations which are equal to the set number are stored, 
while those combinations whose combination numbers lie between the upper 
and lower number limits are searched for and all or any of them are 
stored. The combination weights in these combinations which are stored 
under the condition of equality or lying between the upper and lower 
limits are calculated and stored, and the stored combination weights are 
divided respectively by their combination numbers to provide unit weights, 
and the average of these unit weights is calculated to provide a new unit 
weight. 
The fifth method of finding new unit weights comprises the steps of 
calculating combinations, storing all said combinations and combination 
weights, dividing all the stored combination weights respectively by their 
combination numbers to provide unit weights, and calculating the average 
of these unit weights to provide a new unit weight. 
The sixth method of finding new unit weights comprises the steps of 
calculating the sum of individual combination weights, e.g., the 
combination weights of all or any of those combinations whose combination 
numbers lie between the upper and lower number limits to provide the total 
weight, adding up their combination numbers to provide the total number, 
dividing said calculated total weight by the total number to provide a 
unit weight, and using said unit weight as a new unit weight. 
While the first through sixth methods are based on combination weights, it 
is also possible to calculate new unit weights with the weight of the 
articles in each weighing machine taken into account. This will now be 
described as the seventh through tenth methods. 
The seventh method of finding new unit weights comprises the step of 
dividing the weight of articles measured by a particular one of the 
weighing machines taking part in combinatorial counting operation by the 
number of the articles in said particular weighing machine, thus providing 
a new unit weight. This calculated new unit weight is used in the next 
combinatorial counting to calculate the number of articles from the weight 
of articles received in each weighing machine. 
The eighth method of finding new unit weights is characterized in that in 
the seventh method, the one weighing machine used for finding a new unit 
weight is changed with one selected from the other weighing machines 
taking part in combinatorial counting in a predetermined order for each 
counting operation. 
The usefulness of the eighth method is the removal of the disadvantage of 
fixing one weighing machine used for finding new unit weights. More 
particularly, with said one weighing machine fixed, if the articles in 
this particular weighing machine are not discharged in a series of 
operations, this means that the new unit weight is not renewed, failing to 
represent the unit weight of the present articles. 
The nineth method of finding new unit weights comprises the steps of 
dividing the weights of articles in all or any of the n weighing machines 
respectively by the numbers of these articles to find unit weights, 
calculating the average of these unit weights, and storing said average as 
a new unit weight. 
The tenth method of finding new unit weights comprises the steps of 
calculating the total weight by adding up the weights of articles in all 
or any of the n weighing machines, calculating the total numbers by adding 
up the numbers of articles in these weighing machines, and dividing the 
calculated total weight by the calculated total number to provide a new 
unit weight. 
The eleventh method of finding new unit weights will now be described. 
The first through tenth methods of finding new unit weights described above 
comprise the steps of converting weights found by the weighing machines 
into numbers, calculating combinations of these numbers, discharging the 
articles from the weighing machines corresponding to a particular 
combination which satisfies the conditions, recalculating a unit weight, 
storing the latter for use as a unit weight for the next combinatorial 
counting operation. Upon careful examination of the same, it is seen that 
all of the weights found by the weighing machines are newly stored and 
divided by the newly stored unit weight to find respective numbers. 
However, the discharge of articles on the basis of the result of the 
preceding calculation is not from all of the weighing machines. That is, 
there are weighing machines in which articles from the preceding 
combinatorial counting remain without being discharged. However, the next 
calculation is performed by using the newly stored unit weight for 
conversion of weights measured by the weighing machines into numbers. As a 
result, there are weight values not divided by proper unit weight, forming 
a major cause of errors in calculating the number of articles. To elimnate 
this drawback, the conversion into numbers by the use of a newly stored 
unit weight in the next calculation should be limited to those weighing 
machines which were emptied last time and newly filled with articles. That 
is, the eleventh method of finding new unit weights is characterized in 
that for the weighing machines which did not discharge last time, 
calculation for conversion by the use of the new unit weight is not 
performed and instead the numbers into which weights were converted last 
time are stored and used as such for calculation of combinations. If 
calculation of combinations is performed by the use of the stored numbers, 
for those weighing machines which have not discharged, until they 
discharge, the probability that numbers are mistaken because of the 
factors described above can be minimized. In addition, the eleventh method 
of finding new unit weights is performed together with any of the first 
through tenth methods. 
Operation in which the eleventh method of finding new unit weights is 
performed in the arrangement shown in FIG. 1 will now be described with 
reference to the flowchart of FIG. 3. The difference of the flowchart of 
FIG. 3 from that of FIG. 2 is in the region extending from the start of 
calculation of combinations to the point where the arithmetic control 
section 4 stores those combinations which agree with the set number. This 
different operation alone will be described. When a start signal a is 
transferred to the arithmetic control section 4 from a packaging machine 
(not shown), the arithmetic control section 4 outputs a selection signal b 
to the multiplexer 2. In accordance with the selection signal b, the 
multiplexer 2 picks up only those of the weighing machines 1.sub.1 . . . 
1.sub.n which discharged last time and successively transfers analog 
weight voltages to the A/D converter, the A/D converted weights being 
stored in the arithmetic control section 4. The arithmetic control section 
4 divides the stored weights by the unit weight set by the weight setting 
section 5, rounds the quotients to the nearest integers, and converts the 
weights of the articles in the weighing machines 1.sub.1 . . . 1.sub.n 
which discharged last time. In accordance with all of the combination 
codes, the arithmetic control section 4 calculates combination numbers by 
performing predetermined addition from the numbers already stored for the 
weighing machines 1.sub.1 . . . 1.sub.n which discharged last time and the 
numbers which were converted and stored in the last calculation for the 
weighing machines which did not discharge last time, and stores these 
combination numbers and combination codes in pairs. The operation which 
follows is exactly the same as that described with reference to FIG. 2. 
The twelfth method of finding new unit weights will now be described. 
The first through eleventh methods of finding new unit weights employ the 
way of storing a unit weight anew for each combinatorial counting 
operation. However, it does not necessarily follows that the unit weight 
is substantially equal for each combinatorial counting operation or is 
increasing or decreasing in the same direction. For example, if the unit 
weight repeats increase and decrease for each combinatorial counting 
operation, it follows that with respect to the unit weight stored anew in 
a state where it changed in the increasing direction (decreasing 
direction) in the last combinatorial counting operation, the unit weight 
of articles which take part in combinatorial counting operation this time 
is changing in the decreasing direction (increasing direction), i.e., in 
the opposite direction. In this case, the result is that the unit weight 
is stored anew in the direction which lowers the accuracy of conversion 
into numbers. To solve this problem, according to the twelfth method of 
finding new unit weights, renewal storage of unit weight is not effected 
each time and instead unit weights obtained in n successive combinatorial 
counting operations are stored and after the nth time, the average of 
these n unit weights will be stored for use as a new unit weight for the 
following n successive combinatorial counting operations. If renewal 
storage of unit weight is effected every nth time in this manner, the 
probability of number conversion can be increased. 
In addition, the twelfth method of finding new unit weights will be used 
with any of the first through eleventh methods used in the arrangement 
shown in FIG. 1 or will be used with any combination of these methods. 
Operation in which the twelfth method of finding new unit weights is 
performed in the arrangement shown in FIG. 1 will now be described with 
reference to the flowchart of FIG. 4. The difference of the flowchart of 
FIG. 4 from that of FIG. 2 is in the region extending from the point where 
the arithmetic control section 4 transfers discharge signals to weighing 
machines to the point where it waits for a start signal a from the 
packaging machine. This different operation alone will be described. When 
the arithmetic control section 4 outputs a discharge signal, the same 
number of articles as the set number are discharged from the weighing 
machines corresponding to the discharge signals. At this time, the 
arithmetic control section 4 calculates a unit weight (A) by dividing the 
combination weight, which is equal or closest to the weight of the 
discharged articles, i.e., the set weight, by the number of discharged 
articles, i.e., the set number, stores said unit weight (A), and judges 
whether or not the number of times of calculation of such unit weight (A) 
reaches the preset number n. If it does not reach the number n, the 
arithmetic control section waits for a start signal a from the packaging 
machine, performing the next combinatorial operation in the same procedure 
as described with reference to the flowchart of FIG. 2. If the number of 
times of calculation of unit weight (A) reaches the number n, the 
arithmetic control section adds up the n unit weights (A), which have been 
stored, and divides the sum by n, to find the average unit weight, which 
is then used as a new unit weight for the following number conversion. 
Thus, a new unit weight is calculated every nth time, and the same 
procedure is repeated. 
While the arrangement shown in FIG. 1 is an example in which all of the 
data to be processed are once converted into digital values, which are 
then processed by arithmetic operations, it goes without saying that the 
present invention is also applicable to an arrangement for processing 
analog values by arithmetic operations. 
FIG. 5 shows a system in which analog weight voltages from n weighing 
machines 11.sub.1 . . . 11.sub.n are transferred to an arithmetic control 
section 14 through a storage section which stores analog weight voltages. 
The numeral 15 denotes a unit weight setting section for setting the unit 
weight of articles by analog voltage; 16 denotes a number setting section 
for setting by analog voltage the number of articles to be discharged; 17 
denotes a weight setting section for setting by analog voltage the total 
weight of that number of articles which is set by the number setting 
section 16; 18 denotes an upper weight limit setting section for setting 
by analog voltage the upper limit of the total weight of a set number of 
articles; and 19 denotes a lower weight limit setting section for setting 
by analog voltage the lower limit of the total weight of a set number of 
articles. When a start signal from a packaging machine (not shown) adapted 
to package counted articles is transferred to the arithmetic control 
section 14, combinatorial counting operation is performed in the same 
manner as described with reference to the arrangement of FIG. 1, and a new 
unit weight is calculated by any of the first through twelfth methods of 
finding new unit weights or by any combination thereof. 
In addition, in the present invention described above, a combination whose 
combination number is equal to the set number is found; however, a 
combination which is closest to the set number may be found. In this case, 
however, since the combination which is closest to the set number is not 
always equal to the set number, a new unit weight will be calculated by 
dividing the combination weight by said closest number. 
Further, of the combinations whose combination numbers are equal or closest 
to the set number, any one combination without regard to the combination 
weight, e.g., a combination initially found to be equal to the set weight 
may be used to discharge articles. In this case, therefore, said upper and 
lower weight limit setting sections and weight setting section are not 
needed. 
Further, in the present invention described above, during combinatorial 
operation, only that one of the combinations calculated previously whose 
combination number is equal or closest to the set number is stored, and 
upon completion of all combinatorial operations, a combination whose 
combination number is equal or closest to the set number in all 
combinations may be found. 
As many apparently widely different embodiments of this invention may be 
made without departing from the spirit and scope thereof, it is to be 
understood that the invention is not limited to the specific embodiments 
thereof except as defined in the appended claims.