Math Field Day California State University, Fresno April 22, 2006

Contests

• Mad Hatter Marathon is an individual contest.

  The Mad Hatter Marathon is a competition in rapid computation and solution. Problems will be shown on a screen, and also read aloud. The questions will be given in a multiple choice format. The student will work on the problems mentally, if possible, but using paper and pencil is allowed. There will be two parts, 60 min long each. Each part will consist of 40 problems, thus approximately 1.5 min will be given for each question.

  • Mad Hatter 11-12 is for grades 11-12. (Lower grades are allowed to participate in this contests, however, are encouraged to participate in one of the other Mad Hatters which are very similar in nature, but are open only to lower grades only.)

    Problems will be 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.

    Sample problems     MH A 2005 problems, part I     MH A 2005 problems, part II     Contestant instructions

  • Mad Hatter 9-10 is for grades 9-10. (Lower grades are allowed to participate in this contests, however, are encouraged to participate in Mad Hatter 6-8 which is very similar in nature, but is open only to lower grades only.)

    Problems will be chosen from applied as well as academic math. Contest material will be restricted to topics covered in foundation courses in algebra and geometry. Other problems will be utilized if the solutions are primarily "intuitive" in nature.

    Sample problems     MH B 2005 problems (both parts)     Contestant instructions

  • Mad Hatter 6-8 is for grades 6-8. (Grades 5 and lower, however, are allowed to participate in this contests.)

    Problems will be chosen from applied as well as academic math. Contest material will be restricted to topics covered in foundation mathematics courses. Other problems will be utilized if the solutions are primarily "intuitive" in nature.

    Sample problems     Since this is the first year we have this contest, no previously used problems are available.

• Leap Frog

  Knowledge of mathematics and excellence in the skills of checking, working clearly and neatly, and making best use of the time will be recognized in this contest.

  Two-person teams are entered with each person working different sets of approximately 10 problems during the first part. At the end of 60 minutes, 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 will be used to determine team placement.

  • Leap Frog 9-12 is a team contest for grades 9-12. (Each team consists of 2 students from the same school. Lower grades are allowed to participate in this contests, however, are encouraged to participate in Leap Frog 6-8 which is very similar in nature, but is open only to lower grades only.)

    Problems will be chosen from all high school subjects in mathematics and some will require original thinking. Topics covered will include: geometry, number theory, algebra, permutations, combinations, probability, exponents and logarithms, trigonometric (circular) functions, and no more than 10% of miscellaneous topics.

    Sample problems     LF 2005 problems, part I     LF 2005 problems, part II     Contestant instructions

  • Leap Frog 6-8 is for grades 6-8. (Grades 5 and lower, however, are allowed to participate in this contests.)

    Sample problems     Since this is the first year we have this contest, no previously used problems are available.

• Game Tournament is an individual contest for grades 6-12.

  This contest is a tournament held in two 1 hour periods with a short break between them. During the first period, contestants will play this game (against each other). The contestants are expected to know the rules of this game and have a strategy in mind. Top players will play another game during the second period. The second game will be a variation of the first one. Here are some possible variations. However, our second game does not have to be one of these but it may be a different variation. The exact rules of the second game will be announced at the end of the first period, so the contestants can think of a strategy during the break.

  The eliminated players may either watch the remaining contestants, play these or other games among themselves (only their scores will no longer be recorded), or watch math videos in another room. There will be math majors there to keep them busy...

  Here are some more details: For all games, the initial positions of the tokens will be given by the organizers.
  The contestants will be randomly divided into small groups (approximately 5-8 players, depending on the total number of participants). Each contestant will play with each (or almost each) of the other players in his or her group twice. More precisely, each (or almost each) pair in the group will play two times where the first time one of the players choses whether he or she wants to go first or second, and the second time the other player choses whether he or she wants to go first or second. All scores will be recorded. All players will have played the same number of games by the end of the first hour (perhaps about 8-12 games, exact number to be determined). Top players (the exact number to be determined, depending on the total number of participants) will proceed to the second half of the tournament.
  Exact rules of the second game will be announced, and then we will take a short break (about 10-15 minutes). After the break, the contestants will again be divided into small groups (perhaps a bit smaller than in the first hour) and play the second game in the same fashion as before. After each group is done, total scores from first and second part of the tournament will be counted for each participant. This total score will be the participant's score used to determine winners and school rankings. If there are any ties for the first, second, or third places, 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.

  Contestant instructions