G285 2021 Fall Problem Set
Welcome to the Fall Problem Set! There are problems, multiple-choice, and free-response.
Larry is playing a logic game. In this game, Larry counts , and removes the number for every th move, skipping for , and then increments by one. If starts at , what is when Larry counts his th integer? Assume
Let be a right triangle with right angle at , and . Let denote the intersection of the cevian dropped from onto such that . If the reflection of point across lies on the circumcircle of as , , and the circumradius of is an integer, find the smallest possible value of .