Penn Math Contest IV

Penn Math Contest IV will take place both in-person at David Rittenhouse Laboratory @ The University of Pennsylvania and online. We are limiting both competitions to 300 students each.
PMC is split into 3 difficulty levels: Beginner, Intermediate, and Advanced.
There is an individual and a team round.
- You may register either as an individual or as a team of up to three. If you have a team, then we request that each member of the team fills out the form separately. If you do not have a team, then we will either match you up with other competitors who do not have a team for the team round, or, if you prefer, you can participate in the team round by yourself. For any questions about registration, feel free to email us at pennmathcontest@gmail.com!
The top five individual students in the in-person contest will get medals, and the top three individual students in the in-person contest will get a book prize! The top three individual students and the top team in each category (either in-person or online) will also get a virtual certificate.

Beginner is aimed at students competing in a math contest for the first time, or with little-to-no prior experience, mirroring the MATHCOUNTS level.
Intermediate is the average difficulty level for most participants, mirroring the AMC 10/12 level.
Advanced is for experienced competitors, who want more of a challenge. If you don't know which difficulty is best for you, feel free to take a look at some problems from each difficulty level!

You are only allowed to use writing utensils, blank scratch paper, and (optionally) a ruler and compass. Do not use any devices that would give you an unfair advantage, such as calculators, computers, protractors, or phones.
You are not allowed to consult outside sources such as the Internet or other people while you participate in the contest. The only exception is that for the team rounds, you are permitted to talk and collaborate, but only with members of your team.
While you are participating in the contest online, your camera should be turned on to allow our proctors to monitor potential cheating. Both your face and your work surface should be visible at all times.
All questions are worth the same amount of points. If you get stuck on a question, feel free to skip it and move on to the next question!
In the case of a tie, certain problems have been designated as tiebreaker questions. Those problems are denoted by a star next to the problem number. If two students tie, whoever solved the most tiebreaker questions will place higher.
If there end up being cases which we haven’t thought of and are not addressed by the rules, we will use our best common sense and judgment to sort the situation out. We will try to be as fair as possible.