It’s called a diophantine equation, and it’s sometimes known as the “summing of three cubes”: find x, y, and z such that x³+y³+z³=k, for each k from 1 to 100.

Over the course of the school year, you keep track of how much snow falls on a given day and whether it was a snow day. your data indicates that of twenty-one days with less than three inches of snow, five were snow days, while of the eight days with more than three inches of snow, six were snow days. if all you know about a day is that it is snowing, what is the probability that it will be a snow day?