A favorite hamburger joint of mine has the following 15 choices for toppings:
After much experimentation, I’ve decided that three toppings is about the right number to have on any one burger (too many toppings masks the flavor of the burger itself). So, being a mathematician, I’ve decided that I should try all possible combinations of 3 toppings. Here are the problems then:
1) If I visit the burger joint once a week (ordering one burger per visit), how long will it take me to reach my goal?
2) Can you devise an algorithm for working through all combinations that is not too complicated and provides a reasonable amount of variation (for instance, I don’t want to have 13 visits in a row where I have mayo and relish and one other topping. I probably don’t even want that for two or three visits in a row).