Department of Mathematics

# Math Field Day Contests

At Math Field Day, participants can compete in one of three contests:

• Leap Frog Relay (grades 6-8, 9-10, 11-12)
• Game Tournament (grades 6-8, 9-12)

The Mad Hatter Marathon is an individual contest.  It is a competition in rapid computation and solution. Problems are shown on a screen, and also read aloud. The questions are in a multiple choice format. Competitors will work on the problems mentally, if possible, but using paper and pencil is allowed. There are two parts. Each part consists of 30 problems, with 2 minutes (1.5 minutes for grades 6-8) given for each question.  Thus each part runs approximately 60 minutes (45 minutes for grades 6-8).

Mad Hatter 11-12 is for grades 11-12. (Students in lower grades are allowed to participate in this contest.  They are encouraged, however, to participate in Mad Hatter 6-8 or Mad Hatter 9-10, as appropriate, which are very similar in nature but are open to lower grades only.)

Problems are chosen from applied as well as academic math. The following topic areas should be reviewed by participating students: binomial expansion, complex numbers, functions (polynomial, rational, algebraic, circular, logarithmic, exponential), geometry (plane, space, coordinate), number theory, progressions, combinations, probability, sequences, series, and trigonometry.

#### Problems from Previous Mad Hatter 11-12 Contests

Mad Hatter 9-10 is for grades 9-10.  (Students in grades 8 and lower are also allowed to participate in this contest. They are encouraged, however, to participate in Mad Hatter 6-8, which is very similar in nature but open to students up to 8th grade only.)

Problems are chosen from applied as well as academic math. Contest material is restricted to topics covered in foundation courses in algebra and geometry. Other problems whose solutions are primarily "intuitive" in nature may be used.

#### Problems from Previous Mad Hatter 9-10 Contests

Mad Hatter 6-8 is for grades 6-8. (Grades 5 and lower are also allowed to participate in this contest.)

Problems are chosen from applied as well as academic math. Contest material is restricted to topics covered in foundation mathematics courses. Other problems whose solutions are primarily "intuitive" in nature may be used.

## Leap Frog Relay

Leap Frog Relay is a team of two contest.  Knowledge of mathematics and excellence in the skills of checking, working clearly and neatly, and making best use of the time are tested in this contest.

There are two parts.  Two-person teams compete, with each person working on different sets of 10 problems during the first part. The problems are in a multiple choice format.  No communication between teammates is allowed.  At the end of 60 minutes there is a short break. Then, for the second part, papers are exchanged and each person is allowed 60 minutes to check, correct, and complete their partner's work. During this checking period, teammates may talk quietly and share ideas. The total score for both papers determines team placement.  Both students must be from the same school to count towards school totals.

### Leap Frog 11-12

Leap Frog 11-12 is a team contest for grades 11-12. (Students in lower grades are allowed to participate in this contest.  They are encouraged, however, to participate in Leap Frog 6-8 or Leap Frog 9-10, as appropriate, which are very similar in nature but are open to lower grades only.)

Problems are chosen from all high school subjects in mathematics; some will require original thinking. Topics covered include: geometry, number theory, algebra, permutations, combinations, probability, exponents and logarithms, trigonometric (circular) functions, and miscellaneous topics.

#### Problems from Previous Leap Frog 11-12 Contests

Some of the problems below are from previous Leap Frog 9-12 contests which have since been replaced by Leap Frog 11-12 and Leap Frog 9-10.

 2023 Leap Frog 11-12 Problems and Solutions 2022 Leap Frog 11-12 2022 Leap Frog 11-12 Solutions 2017 Leap Frog 11-12 2017 Leap Frog 11-12 Solutions 2015 Leap Frog 11-12 2012 Leap Frog 9-12 2011 Leap Frog 9-12 2010 Leap Frog 11-12 2009 Leap Frog 9-12 2008 Leap Frog 9-12

### Leap Frog 9-10

Leap Frog 9-10 is for grades 9-10. (Students in grades 8 and lower are also allowed to participate in this contest.)

#### Problems from Previous Leap Frog 9-10 Contests

 2023 Leap Frog 9-10 Problems and Solutions 2022 Leap Frog 9-10 2022 Leap Frog 9-10 Solutions 2017 Leap Frog 9-10 2017 Leap Frog 9-10 Solutions 2015 Leap Frog 9-10

### Leap Frog 6-8

Leap Frog 6-8 is for grades 6-8. (Grades 5 and lower are also allowed to participate in this contest.)

#### Problems from Previous Leap Frog 6-8 Contests

 2023 Leap Frog 6-8 2023 Leap Frog 6-8 Solutions 2017 Leap Frog 6-8 2017 Leap Frog 6-8 Solutions 2015 Leap Frog 6-8 2012 Leap Frog 6-8 2011 Leap Frog 6-8 2010 Leap Frog 6-8 2009 Leap Frog 6-8 2008 Leap Frog 6-8 2006 Leap Frog 6-8

## Game Tournament

The Game Tournament is an individual contest.  The contest is a tournament of two-person games, held in two 1-hour periods with a short break between them. During the first period, contestants play one of these games (against each other). The contestants are expected to know the rules of these games and have a strategy in mind. Top players from the first part play another game during the second period. The second game is a variation of the first one. Here are some sample game variations. The second game may or may not be one of these. The exact rules of the second game are announced after the break between games, so the contestants must think of a strategy fast.

The eliminated players may either watch the remaining contestants, or play these or other games among themselves (their scores are not recorded).

Here are some more details: For all games, the initial numbers and/or positions of the tokens are given by the organizers.

The contestants are randomly divided into small groups (approximately 5-8 players, depending on the total number of participants). Each contestant plays with each (or almost each) of the other players in their group twice. More precisely, each (or almost each) pair in the group will play two times where the first time one of the players chooses whether they want to go first or second, and the second time the other player chooses. All scores are recorded. All players play the same number of games by the end of the first hour (about 8-12 games; exact number depends on the number of participants and how long the games take to play). Top players (exact number depends on the number of participants) proceed to the second half of the tournament.

After a short break (about 10-15 minutes), exact rules of the second game are announced.  Remaining contestants are again divided into small groups and play the second game in the same fashion as before. After each group is done, total scores from the first and second parts of the tournament are counted for each participant. This total is the participant's score used to determine winners and school rankings. If there are any ties for the first, second, or third place, then (1) a person who never lost two games to the same person (in the same hour) wins over a person who did, and (2) additional games may be used to break ties.

• Game Tournament 9-12 is for grades 9-12. (Students in lower grades are allowed to participate in this contest.  They are encouraged, however, to participate in Game Tournament 6-8, which is very similar in nature but is open to lower grades only.)
• Game Tournament 6-8 is for grades 6-8.  (Grades 5 and lower are also allowed to participate in this contest.)