in fact, it's not that far removed from the st. ives riddle our children at the gate were talking about. both of these problems have elegant solutions by the recognition of the simple pattern of the powers of seven that we see. now, several 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