centuries later, we find slightly more sophisticated kinds of problems and solutions in 6th-century b.c. india. the medical treatise sushruta samhita gives us this problem: how many combinations can be made out of six different tastes: bitter, sour, salty, sweet, astringent, and hot? by taking them one at a time, two at a time, three at a time, and so on, we learn that there are in fact 63 combinations. this was important in ayurvedic medicine because it gave ancient physicians a way to work out which medical substance would best match a patient's ailments. now, there are two things that are going on here. on the one hand, we're asking for the number of possible combinations, or subsets, of the six different spices. this number, as we see, is 63, which is 2^6 - 1. now, notice the sixth power and six spices. there's a pattern here: number goes to power. the magic is that we're seeing a formula, a quick way to answer the question of how many combinations of spices without actually listing them. now, there's a more particular problem that was of interest to the indian doctors, and that was the in