This one is the classic jumping frog with state diagrams, this time in the coordinate plane between a fence and river.
Find the least positive integer such that is a product of at least four not necessarily distinct primes.
A strictly increasing sequence of positive integers has the property that for every positive integer , the subsequence is geometric and the subsequence is arithmetic. Suppose that . Find .
Define a sequence recursively by and for integers . Find the least value of such that the sum of the zeros of exceeds .
While watching a show, Ayako, Billy, Carlos, Dahlia, Ehuang, and Frank sat in that order in a row of six chairs. During the break, they went to the kitchen for a snack. When they came back, they sat on those six chairs in such a way that if two of them sat next to each other before the break, then they did not sit next to each other after the break. Find the number of possible seating orders they could have chosen after the break.
I could not find a great solution to the 2020 AIME II #12, so I created a video solution myself. It is a nice geometric problem with lots of inequalities.