Contest Details

The 2020 Michigan Lemma Math Competition was held on Saturday, January 25, 2020. The contest took place at the University of Michigan Department of Mathematics, located in East Hall: 530 Church Street, Ann Arbor, MI 48109. Results can be found here.
Rules
The Michigan Lemma is a team-based math competition for high school students. Competitors will compete in teams of four in several different rounds, and will earn points towards their team score. The highest scoring teams will receive prizes. In addition, the top scoring individuals will also receive prizes. All contest problems will be solvable without the use of calculus. Lemma Math Competition encourages critical thinking, problem solving, creativity, teamwork, and collaboration. We are against unsportsmanlike conduct and calculators.

Proposition 1: Power Round

The Power Round is a team-based round in which contestants will have 60 minutes to answer a set of open-ended mathematical questions. This round differs from other rounds in that instead of providing a single, numerical answer, students will write a mathematical proof to justify their solutions. The round will explore a mathematical concept, and students will prove expository results about the topic. The Power Round will be graded not only on correctness, but also clarity and comprehensiveness of solutions. The Power Round is worth 50% of the team score.

Proposition 2: Team Round

The Team Round is a team-based round where students will work together to collectively solve 10 problems in 20 minutes. All problems in this round are weighted equally, and the problems will be roughly arranged in order of difficulty. These problems will consist of a wide variety of mathematical topics, and due to the short duration of the round, teams will have to collaborate effectively in order to do well. The Team Round is worth 30% of the team score.

Proposition 3: Individual Round

The Individual Round is an individual round in which students will solve 10 problems in 50 minutes. All problems in this round are weighted equally, and the problems will be roughly arranged in order of difficulty. These problems will consist of a wide variety of mathematical topics. Each student's score will contribute to 5% of the team score, for a total of 20%.

Proposition 4: Wolverine Round

The Wolverine Round is a fun round aimed to allow students from different teams to work together and meet other students interested in mathematics. Students will be randomized into teams, and will have 60 minutes to solve 30 problems, divided into 10 sets of 3 problems each. Each team must submit their answers to a set before receiving the next set, and once a set is submitted, teams cannot return to a previous set. Problems will be weighted roughly by difficulty, and later problem sets will roughly be more difficult. The highest scoring teams in the Wolverine Round will receive prizes.

Proposition 5: Tiebreaker Round

The Tiebreaker Round is a round which will serve as a tiebreaker for the highest scoring indiviuals. Competitors will receive three problems, and allowed to begin at the same time. When a competitor submits their answers, their time will be recorded, and ties will be broken first by number of correct answers and then by order. This round does not affect team scores.

Schedule
8:00 – 8:30 Registration
8:30 – 9:00 Opening Remarks
9:00 – 10:00 Proposition 1: Power Round
10:10 – 10:50 Proposition 2: Team Round
11:00 – 12:00 Proposition 3: Individual Round
12:00 – 1:00 Lunch
1:00 – 2:15 Proposition 4: Wolverine Round
2:30 – 3:30 Math Club Talk
2:30 – 3:30 Proposition 5: Tiebreaker Round
4:00 – 5:00 Awards and Closing Remarks