Day Before the Test: Last Advice and 2019 AMC 10 A, Problem 18

My Last Advice on some key topics asked by commenters before the test especially on what your prep time should look like in the last 48 hours. I really wanted to show how to handle a question that you have no idea how to do, but in the moment you devise a strategy to figure it out. I demonstrate that in the problem that follows the initial topics of last 48 hours prep. If you haven't seen it recently, re-watch the AIME Mindset video either the day before or the day of the test:    • AIME Mindset: The mental preparation you n...   Sohil Rathi's handout discussed and linked here: https://artofproblemsolving.com/commu... Specific Statistics to the Problem 18. Only 7.42% of test takers got it correct and it was skipped by 73.72% of all test takers. My response to whether people will cheat asked by a commenter: "This is a fair question. I think from a youthful perspective it can be a little more alarming than for someone with the benefit of more life experience. Similar posts have been found on the AMC Forums and one of the moderators responded with the following quote from the MAA Director. I will copy and paste that quote along with my further thoughts after it: http://amc.maa.org/amc1012/2013/2013A... "The mission of the MAA Competitions is to increase interest in mathematics and to develop problem solving through a fun competition. Students gain the opportunity to learn and achieve through competition with students in their school and from around the world. Teachers and schools benefit from the chance to challenge students with interesting mathematical questions that are aligned with curriculum standards at all levels of difficulty." Cheating at the AMC contests is pointless and stupid, and those who engage in it, or even discuss it have completely missed our purpose, the purpose of education, and the joy of learning. Lift your heads up. -- Steve Dunbar MAA Director, American Mathematics Competition I fully agree with the above and look at Director Dunbar's remarks as extremely wise and demonstrative of leadership. My additional thoughts are the following. In life there are things you can control and things you cannot. We can control our decisions and we can control our emotions in regards to the events that occur around us. We cannot control the decisions of others. Is it possible people will cheat? It is. Is there anything you can do about it? No. If I was competing at something where other individuals may or may not cheat, I would strive to beat them despite their cheating. It would make the victory that much sweeter. Ask yourself if you cheated and you received an achievement...how would you feel on the other side of that as praise is heaped upon your shoulders for something you didn't really accomplish? If you have integrity or character of any kind it would rob you of the feeling of accomplishment. It would nag at your mind for likely several years whenever you thought back to the experience and praise you had received. You would feel like a fraud. See the Steroids era of baseball in the 90's and why anyone who juiced was not allowed into the Hall of Fame up until this point. Their "success" is tainted. As would be yours. So let's say they cheat and "succeed" and you don't and "fail". I would argue it's actually the opposite. They revealed who they are...a failure who had to cheat to win. You revealed who you are...a person of strong character without the "achievements" of an award in a Math Competition. But you achieved something more. The foundation of character. The foundation of integrity. You won't have a piece of paper or praise from the masses. But you will know who you are. A person who strives to do what is right. Which is more valuable to you? Choose wisely. Start of 2019 AMC 10A Problem 18: 21:03 I may earn commissions for purchases made through the links below. Intro to Number Theory from AoPS: https://artofproblemsolving.com/store...