We saw that one way to determine all of the possible combinations of *n* items taken *k* at a time is to list them according to a certain procedure, called *prastāraḥ* or “spreading out.” This procedure assigns a serial number to each of the possible combinations. Now supposing you don’t want to do the entire *prastāraḥ*, but simply want to figure out the combination that occurs at a given serial number. For instance, among the combinations of 4 syllables, each of which can be either light (।) or heavy (ऽ), what is the exact combination that occurs at serial number **13** in the *prastāraḥ*?

The procedure for finding out this “lost” (*naṣṭaḥ*) pattern is as follows:

- Start with the
**serial number**of the lost pattern (*r*). - For each position in the pattern:
- if the number is
**even**, the syllable in the position is**light**; divide this number by 2, and return to step 2; - if the number is
**odd**, the syllable in the position is**heavy**; add one to this number, then divide the sum by two, and return to step 2.

Hence for *r* = 13 in the *prastāraḥ* of four positions (*k* = 4):

**First syllable**: 13 is odd, hence**heavy**(ऽ).**Second syllable**: (13+1)/2 = 7 is odd, hence**heavy**(ऽ).**Third syllable**: (7+1)/2 = 4 is even, hence**light**(।).**Fourth syllable**: 4/2 = 2 is even, hence**light**(।).

Hence the lost pattern is ऽऽ।।, which can be verified in the *prastāraḥ* given as an example in the previous post.