Demonstration in Chinese and Vietnamese mathematics 543
cannot be applied to all [the functionaries]. Th is is why [one] does not
need to ‘dispose and arrange’ [the counting rods in order to solve the
problem in this way] and [can]
[3] trust [what was stated] in the problem [viz., that the fl at-rate distribu-
tion method cannot be used]. It is already clear that this is so! Also,
ranging the people according to their unequal capacities, [one has to
give them] larger or smaller
[4] awards. So, those who are superior will obtain more, those who are
inferior will obtain less. One distributes it [according to]
[5] unequal ranks. Th e [distribution] pattern certainly [should be] like
this. Th erefore [one will] use this amount of 5292
[6] lượng to distribute this [money] among the aforementioned corpus of
328 persons [while applying] the ‘weighted distribution’ [method] and
having the number of the people subdivided into
[7] three ranks. Rank A: 8 persons, each person obtains 7 parts. Rank B: 20
persons, each person obtains
[8] 5 parts. Rank C: 300 persons, each person obtains 2 parts. Th is is the
method of ‘weighted distribution’ for [this] problem.
[9] Th is method should be applied [as follows]: fi rst of all, [I] 85 set [on the
counting device] 8 persons of rank A, multiply them by 7 parts, obtain
the product, 56
/p. 32a/
[1] parts–multiples. 86 Again [I] set 20 persons of rank B, multiply them by
fi ve parts, obtain the product, 100
[2] parts–multiples. Also [I] set 300 persons of rank C, multiply them by
two parts, obtain the product, 600 parts–multiples.
[3] Th en in an auxiliary [position of the counting instrument I] add the
three [amounts] of parts–multiples, and obtain in total 756 parts–
multiples.
[4] [I] take it as the ‘norm’ [= divisor]. And at this moment [I] set 5292
lượng of this money to be the dividend. Th en
[5] [I] divide [this dividend] by the norm, set it [= the result, on the count-
ing instrument], and [thus] obtain [that] one part–multiple equals
seven lượng. [I] keep it [on the counting instrument] as the ‘constant
norm’ and multiply by it
85 I translate this part of the examination paper in fi rst person, since its imaginary author is
assumed to perform operations with a counting device (hence ‘set’) and to comment on them.
86 On the term ‘part–multiple’ (Chinese fenlü ) see the discussion above, pp. 529–30.