530 alexei volkov
‘parts– multiples’ (or ‘multiples of parts’?) fenlü introduced by the
Vietnamese author appears to be unparalleled in the Chinese mathematical
texts of the fi rst millennium ce.
Th e solution of the imaginary examinee was supposed to be designed as a
modifi cation of the solution of a problem from the treatise he, presumably,
was supposed to be familiar with. In other words, the examination paper
was based on a problem already solved and discussed earlier, but with a
modifi ed structure (three groups of functionaries instead of the combina-
tion of two individual and two collective donators) and altered numerical
data. Th e entire format of the examination paper was larger than just one
problem: it was rather that of a ‘research project’ in which a given situation
was approached with two mathematical ‘models’, one of fl at-rate distribu-
tion (rejected as neither fi tting into the numerical data nor correspond-
ing to the hierarchical structure of the group of functionaries) and one of
weighted distribution.
Th e mathematical contents of the particular problem solved in the
Vietnamese model examination paper are not as important for the present
discussion as the very format of the essay suggested by the author of the
treatise who apparently was well acquainted with the actual examination
procedure. Most importantly for the present discussion, the Vietnamese
model examination paper fi ts, to a large extent, into the format described in
the Tang dynasty Chinese source mentioned above, namely: (1) the core of
the examination task consists of a mathematical problem; (2) the examinee
‘elucidates’ the ‘numerical values’ provided in the given problem (that is,
checks the consistency of the given numerical data), and (3) he ‘designs
a computational procedure’ of which (4) the ‘structure/rationale’ he dis-
cusses in detail, that is, he provides a detailed solution in which every step
is commented upon. Th e imaginary Vietnamese examinee styles his text as
if he operates with a counting instrument to obtain his result while writing
down the results of the operations he is performing. It would be reasonable
to assume that the Chinese candidates of the Tang dynasty also employed
their counting rods during the examination to solve the problems given
to them. If this assumption is correct, their solutions must have contained
the protocols of performed computations that would have looked rather
similar to that found in the Vietnamese model examination paper. Th is
observation makes it tempting to interpret the term lu (‘records, pro-
tocols’) employed in the description of the mathematics examinations in
the Xin Tang shu quoted above as referring to this particular feature of the
mathematics examination papers.