पाटीगणित (श्रीधराचार्य - प्राचीन संस्कृत टीका एवं प्रो. कृपाशंकर शुक्ल सविस्तार व्याख्या)

MIXTURES. SPECIAL PROBLEMS 59
Rule for writing down the combinations of 2 or more savours
in a serial order :
73. To get the 2-savour combinations add the pre-
ceding savour to all the succeeding one’s in order ; and to get
the combinations of 3 or more savours add the preceding
savour to the (succeeding) combinations of 2 or more savours
which do not contain the preceding savour.
Let the six savours be denoted by
a b c d e f .
Then the 2-savour combinations are :
ab, ac, ad, ae, af ; bc, bd, be, bf ;
cd, ce, cf ; de, df ; ef.
The 3-savour combinations are :
abc, abd, abe, abf, acd, ace, acf, ade, adf, aef ;
bcd, bce, bcf, bde, bdf, bef ; cde, cdf, cef ; def.
The 4-savour combinations are :
abcd, abce, abcf, abde, abdf, abef, acde, acdf ;
acef, adef ; bcde, bcdf, bcef, bdef, cdef.
The 5-savour combinations are :
abcde, abcdf, abcef, abdef, acdef, bcdef.
The 6-savour combination is :
abcdef.
(x) CERTAIN SPECIAL TYPES OF PROBLEMS
Rule for solving problems on pillars (stambhoddeśaka¹) or
problems involving remainders (śeṣoddeśaka) :
74(i). To solve problems on pillars or problems involv-
ing remainders, divide the visible quantity (dṛśya) by one minus
(the sum of) the fractional parts (of the whole).²
¹ Mahāvīra calls stambha-jāti by the name bhāga-jāti, and Śrīpati
by the name dṛśya-jāti. See GSS, iv. 4(i) and GT, p. 41, vs. 55.
² Cf. GSS, iv. 4(i); GT, p. 41, vs. 55. Also see GK,I, p. 17, lines 14-19.
Mahāvīra gives a separate rule for the śeṣa-jāti. See GSS, iv. 4(ii). The
same rule is given by Āryabhaṭa II and Śrīpati. See MSi, xv. 20; GT,
p. 44, line 11.