बृहत्संहिता (आचार्य वराहमिहिर - स्थापत्य, खगोल, मौसम व जल विज्ञान)

Adh. LXXVII. Sl. 23.] सप्तसप्ततितमोऽध्यायः 609 columns also. The last number of the last column will reveal the number 1820. (See figure in the margin). The numbers 1, 2, 3......16 in the first column represent respectively the 16 sub- stances mentioned in slokas 13-14, supra (pp. 606-607). Firstly, let the first 3 sub- stances be considered as constant and any one of the remaining as variable. The num- ber of perfumes formed will be 13. Next, taking substances 1, 3, and 4 as constant and one of the rest as variable, we get 12 varie- ties. Proceeding further in the same man- ner, we get 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1 varieties, or 91 in all. Now let the substances 1, 2 and 4 be considered as constants and one of the re- maining as variable, we get 12 perfumes. By taking 1, 3 and 5 as constants, the num- ber will be 11, and so on. The total will thus be 78. Similarly making 1, 2, 5; 1, 3, 6; 1, 4, 7 etc., as constants, we shall get 11, 10, 9, 8, 7, 6, 5, 4. 3, 2, 1 or a total of 66 varieties. Thus we shall get 91, 78, 66, 55, 45, 36, 28, 21, 15, 10, 6, 3, 1 or 455 in all. Proceeding in the same way with other combina- tions, the several totals will be 364, 286, 220, 165, 120, 84, 56, 35, 20, 10, 4, 1 or a grand total of 1820. The process to get at the above figures as enunciated by Bhattotpala in his commentary is circuitous and confusing. This is only the number of combinations of 16 things taken 4 at a time ( ¹⁶C₄ ) or 1820.

द्वित्रिन्द्रियाष्टभागैरगुरुः पत्रं तुरुष्कशैलेयौ । विषयाष्टपक्षदहनाः प्रियङ्गुमुस्तारसाः केशः ॥२३॥ बृ. सं. 77