View source for G285 2021 Fall Problem Set

Welcome to the Fall Problem Set! There are <math>15</math> problems, <math>10</math> multiple-choice, and <math>5</math> free-response. 

==Problem 1==
Larry is playing a logic game. In this game, Larry counts <math>1,2,3,6, \cdots </math>, and removes the number <math>r+p</math> for every <math>r</math>th move, skipping <math>r+jp</math> for <math>j \neq 0 \mod 3</math>, and then increments <math>p</math> by one. If <math>(r,p)</math> starts at <math>(1,3)</math>, what is <math>r+p</math> when Larry counts his <math>100</math>th integer? Assume <math>\{r,p,j \} \in \mathbb{N}</math>

==Problem 2==
Let <math>\triangle ABC</math> be a right triangle with right angle at <math>B</math>, and <math>AC=12</math>. Let <math>D</math> denote the intersection of the cevian dropped from <math>B</math> onto <math>AC</math> such that <math>DA=DC</math>. If the reflection of point <math>B</math> across <math>D</math> lies on the circumcircle of <math>\triangle ABC</math> as <math>E</math>, and <math>\sin(BAC)<\frac{5}[8}</math>, find the smallest possible integer radius of the circumcircle of <math>\triangle EBA</math>.