Click here for this year's Honors Day Schedule, 4/26/08
CLICK HERE FOR 07-08 PROBLEM SETS
WHAT IS MATHEMATICAL TALENT?
Mathematical talent is a combination of ingenuity, insight, creativity, the willingness to experiment, and persistence; it is not merely a skill in manipulation. By working on problems, you can develop your talent for mathematical thinking and problem solving.
MATHEMATICAL TALENT NEEDED
Mathematical talent and problem-solving ability is needed in engineering, physics, chemistry, and other sciences. In fact, with the application of mathematics in business and the social sciences, there is hardly a field that you can enter that does not need a good background in mathematics.
WHY ME?
You can discover how enjoyable being creative can be. You can experience the thrill of solving hard problems. You can learn some new mathematics which is not usually covered in class. You can discover what your own talents in mathematics are if you really give these problems a try.
HOW TO PARTICIPATE
Mail your solution to the address given on each problem set, unfortunately we are not able to accept emailed entries. You do not have to solve all five problems in each set; submit any number that you can do. Do not be surprised if you cannot get them all; some of them are very difficult. You are doing well if you can do any of them. It is not enough to get the "right answer," you also have to provide an adequate explanation of your method and reasons for its correctness. The problem sets are graded; and partial credit is given. Solutions and coded lists of solvers will be sent out later. You can use our solutions as a guide on how to write up your subsequent solutions. After the first time that you send in solutions, we will correspond with you directly. Your student code will appear on the top left hand corner of the mailing label that has your name and address. Please contact us if there are any mistakes.
ENTER AS A TEAM OR AS AN INDIVIDUAL
You can enter the contest either as a team or as an individual. A team consists of two to four people. If any change in the membership of the team is needed, please first inform us by sending email to pomtalsrch@pomona.edu or by calling 909-621-8409. One of the team members acts as the coordinator and will receive the problem sets and be responsible for sending us the solutions. The first time your team enters the contest, you should send us complete information about team members and designate one member as the coordinator. No individual can be on more than 1 team or enter both as an individual and as a member of a team. We will keep overall scores in two separate categories, one for individual participants and one for teams.
SOME SAMPLE PROBLEMS
- A quadrilateral whose consecutive sides have lengths 39, 52, 60 and 25 respectively, is inscribed in a circle. Prove that one of the diagonals of the quadrilateral is a diameter of the circle.
- Find all real numbers a such that the equation x3+ax+10=0 has a solution whose reciprocal is also a solution.
- There are 44 trees arranged in a circle and a bird sitting on each. Once every minute, two birds fly away from the tree they are on. One goes clockwise, the other counterclockwise and each alights on the first tree it comes to. Is it possible for all 44 birds to ever be simultaneously on the same tree?
- Let S be a set of 51 positive integers, each of which is at most 100. Show that S contains a number that is a multiple of some other number in S.
HONORS DAY AT POMONA COLLEGE
The top entrants and their teachers are recognized by Pomona College. We will have an Honors Day at which the students will talk to professors and mathematics students, hear some mathematics and science lectures, get a tour of the campus, attend an Honors Luncheon, and receive some simple prizes. We will invite the top teams as well as the best individual entrants. You don't have to solve all the problems to be invited. In past years, someone who completely solved eight problems in the course of the year would be invited.
HOW TO GET A COPY OF THE PROBLEM SET
Problem sets are now available online! Click Here.
You can also request a copy of the problem set by sending email to pomtalsrch@pomona.edu, with the subject "talent search." Include the following information in your email:
Full Name
Full Home Address
Grade
Full School Address
You can also write to:
Talent Search
Department of Mathematics and Computer Science
Pomona College
610 N. College Way
Claremont, CA 91711
Or call (909)621-8409.
The High School Talent Search is organized by Professor Adolfo Rumbos and Professor Ami Radunskaya
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