On October 29, 2022, the 19-th annual on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the test with solutions, and our report can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2022, Registration form in PDF
- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2022, in PDF
- Our report about UAB MATH TALENT SEARCH DAY in PDF

On November 9, 2019, the 18-th annual on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the test with solutions, and our report can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2019, Registration form in PDF
- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2019, in PDF
- Our report about UAB MATH TALENT SEARCH DAY in PDF

On October 13 of 2018 the 17-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the test with solutions, and our report can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2018, Registration form in PDF
- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2018, in PDF
- Our report about UAB MATH TALENT SEARCH DAY in PDF

UAB Math Talent Search DayOn October 14 of 2017 the 16-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the test and solutions of its problems, and our report can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2017, Registration form in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2017, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2016

UAB Math Talent Search DayOn November 19 of 2016 the 15-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2016, Registration form in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2016, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2015

UAB Math Talent Search DayOn October 31 of 2015 the 14-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2015, Registration form in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2015, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2014

UAB Math Talent Search DayOn November 15 of 2014 the 13-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2014, Registration form in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2014, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Spring 2014

AMC 10 B and AMC 12 B contestsOn February 20, UAB Department of Mathematics hosted AMC 10 B and AMC 12 B contests run by MAA. Overall 28 students from 4 schools participated in the contest. The event was sponsored by the Outreach Program of the UAB Department of Mathematics.

Fall 2013

UAB Math Talent Search DayOn October 19 of 2013 the 12-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2013, Registration form in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2013, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Spring 2013

AMC 10 B and AMC 12 B contestsOn March 01 UAB Department of Mathematics hosted AMC 10 B and AMC 12 B contests run by MAA. Overall 34 students from 3 schools participated in the contest. The event was sponsored by the Outreach Program of the UAB Department of Mathematics.

Fall 2012

UAB Math Talent Search DayOn October 27 of 2012 the 11-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2012, Registration form in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2012, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Spring 2012

AMC 10 B and AMC 12 B contestsOn March 02 UAB Department of Mathematics hosted AMC 10 B and AMC 12 B contests run by MAA. Overall 17 students from 3 schools participated in the contest. The event was sponsored by the Outreach Program of the UAB Department of Mathematics.

Fall 2011

UAB Math Talent Search DayOn October 29 of 2011 the 10-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below. At the Awards Ceremony there was a talk given by a prominent visiting scholar, Professor Dmitriy Dolgopyat from University of Maryland, sponsored by the Outreach Program of the Department of Mathematics of UAB. Professor Dolgopyat talked about continuous fractions. The link to the abstract of his talk can be found below as well.

- UAB MATH TALENT SEARCH DAY, FALL 2011, Registration form in PDF

- The abstract of the talk by Professor D. Dolgopyat, entitled CONTINUOUS FRACTIONS

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2011, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2010

UAB Math Talent Search DayOn November 13 of 2010 the 9-th on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2010, Registration form in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2010, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2009

UAB Math Talent Search Day AnnouncementOn November 21 of 2009 the eighth on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2009, Registration form DOC

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2009, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2008

UAB Math Talent Search Day AnnouncementOn November 15 of 2008 the seventh on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and was implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2008, Registration form DOC

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2008, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2007

UAB Math Talent Search Day AnnouncementOn November 10 of 2007 the sixth on-site math contest called UAB MATH TALENT SEARCH DAY was held at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. The registration form with detailed information, the problems with solutions, and our report about the contest can be found below.

- UAB MATH TALENT SEARCH DAY, FALL 2007, Registration form DOC

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2007, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2006

UAB Math Talent Search DayOn October the 28th of 2006 the fifth on-site math contest called UAB MATH TALENT SEARCH DAY was run at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. Detailed information can be found below.

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2006, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Fall 2005

UAB Math Talent Search DayOn November the 12th of 2005 the fourth on-site math contest called UAB MATH TALENT SEARCH DAY was run at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. Detailed information can be found below.

- Problems and solutions from UAB MATH TALENT SEARCH DAY, FALL 2005, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Winter-Spring 2005

UAB Math Talent Search DayOn February the 19th of 2005 the third on-site math contest called UAB MATH TALENT SEARCH DAY was run at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. Detailed information can be found below.

- Problems and solutions from UAB MATH TALENT SEARCH DAY 2005, 10th grade, in PDF

- Problems and solutions from UAB MATH TALENT SEARCH DAY 2005, 11th grade, in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Winter-Spring 2004

Math-by-Mail Contest 2004Math-by-Mail competition is run by the Outreach Program at the Department of Mathematics at UAB since Spring 2001. This is an individual contest presented by our Outreach Program and designed to test logical thinking and depth of understanding of mathematics by high school students. The contest is open to all high school students from participating schools starting at the freshman level.

If you are interested in the problems and in other details concerning UAB Math-by-Mail Contest 2004 you can download all this information in PDF format.

- Information (including problems with solutions) about UAB Math-by-Mail Contest 2004 in PDF

Contact information:

Dr A. Blokh, Director of
Outreach Program Department of Mathematics University of Alabama at Birmingham Birmingham, AL 35294-1170 (205)934-2154 ablokh@math.uab.edu |

UAB Math Talent Search DayOn February the 7th of 2004 the second on-site math contest called UAB MATH TALENT SEARCH DAY was run at UAB. It was sponsored by UAB Department of Mathematics and implemented by the Outreach Program of UAB Department of Mathematics. Detailed information can be found below.

- Problems and solutions from UAB MATH TALENT SEARCH DAY 2004 in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF

Spring 2003

Math-by-Mail Contest 2003Math-by-Mail competition is run by the Outreach Program at the Department of Mathematics at UAB since Spring 2001. This is an individual contest presented by our Outreach Program and designed to test logical thinking and depth of understanding of mathematics by high school students. The contest is open to all high school students from participating schools starting at the freshman level.

If you are interested in the problems and in other details concerning UAB Math-by-Mail Contest 2003 you can download all this information in PDF format.

- Information about UAB Math-by-Mail Contest 2003 in PDF

Contact information:

Dr A. Blokh, Coordinator of
Outreach Program Department of Mathematics University of Alabama at Birmingham Birmingham, AL 35294-1170 (205)934-2154 ablokh@math.uab.edu |

UAB Math Talent Search DayOn March the 8th of 2003 a new on-site math contest was run at UAB. It was sponsored by UAB Department of Mathematics and UAB School of Natural Sciences and Mathematics which we gratefully acknowledge here. The event (called UAB MATH TALENT SEARCH DAY) was implemented by the Outreach Program of UAB Department of Mathematics with the help of UAB Undergraduate Admissions and Enrollment Management. In addition to the contest it included some other activities as well. Detailed information can be found below.

- Information about UAB MATH TALENT SEARCH DAY in PDF

- Registration form for UAB MATH TALENT SEARCH DAY in PDF

- Problems from UAB MATH TALENT SEARCH DAY in PDF

- Solutions of problems from UAB MATH TALENT SEARCH DAY in PDF

- Our report about UAB MATH TALENT SEARCH DAY in PDF
Train Your Brain Math ClubTrain Your Brain Math Club meets on Fridays at 4:20-5:20pm. The aim is to teach high school students how to solve interesting and often hard but still elementary problems. This should be quite helpful to those of the students who want to succeed in Math Contests such as AMC and ARML.

We use a variety of sources, including the problems from AMC 10 and AMC 12 competitions as well as some other collections of problems. Occasionally, certain topics from more advanced Mathematics (such as elementary Graph Theory, Set Theory or Discrete Mathematics) are considered.

Students who are interested in joining Train Your Brain Math Club should call UAB Special Studies at (205)934-8263 and mention Train Your Brain Math Club.

Contact information:

Dr A. Blokh, Director of Outreach Program

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about Train Your Brain Math Club in PDF
UAB Mathematical School by Correspondence (UAB MASC)The UAB Department of Mathematics and UAB Special Studies are running a UAB Mathematical School by Correspondence (UAB MASC) from October 2002 through April 2003. This initiative is aimed at reaching out to high school students interested in Mathematics. All the details can be found below in the description of the activities run by the Outreach Program of the Department of Mathematics at UAB in the fall of 2002.

Contact information:

Dr A. Blokh, Director of Outreach Program

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about UAB MASC in PDF

Fall 2002

Train Your Brain Math ClubTrain Your Brain Math Club meets on Fridays at 4:20-5:20pm. The aim is to teach high school students how to solve interesting and often hard but still elementary problems. This should be quite helpful to those of the students who want to succeed in Math Contests such as AMC and ARML.

We use a variety of sources, including the problems from AMC 10 and AMC 12 competitions as well as some other collections of problems. Occasionally, certain topics from more advanced Mathematics (such as elementary Graph Theory, Set Theory or Discrete Mathematics) are considered.

Students who are interested in joining Train Your Brain Math Club should call UAB Special Studies at (205)934-8263 and mention Train Your Brain Math Club.

Contact information:

Dr A. Blokh, Director of Outreach Program

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about Train Your Brain Math Club in PDF

UAB Mathematical School by Correspondence (UAB MASC)The UAB Department of Mathematics and UAB Special Studies are running a UAB Mathematical School by Correspondence (UAB MASC) from October 2002 through April 2003. This initiative is aimed at reaching out to high school students interested in Mathematics.

The School is devoted to an in-depth study of Trigonometry. We have chosen this field because it is related to Geometry and Analysis which are major topics in Mathematics. Studying at UAB MASC will allow students to develop a better understanding of these topics and of Mathematics as a whole. The main focus of the School will be on a theoretical study of Trigonometry, and on developing problem-solving skills which can then be applied to all kinds of problems, not necessarily related to Trigonometry. Therefore, studying at UAB MASC could be helpful for preparing for the mathematical part of tests like ACT or SAT.

The main audience of UAB MASC are 10-, 11- and 12-graders, even though as an exception we are willing to consider some 9-graders who have already covered Geometry. The textbook used in the school will be the following:

TRIGONOMETRY

by I. M. Gelfand, Rutgers University, NJ

M. Saul, Bronxville Schools, NY

Birkhauser, Boston-Basel-Berlin, 2001, ISBN 0-8176-3914-4The textbook can be ordered by mail from any major bookseller in the US. I. M. Gelfand, originally from Moscow, currently from Rutgers University, is one of the greatest living mathematicians who devoted a lot of his time to working with high school students. He organized a very successful Mathematical School by Correspondence which has been operating in Moscow for a long time and in which a number of famous Russian mathematicians studied. UAB MASC is modeled after that school and will function as follows:

1. by the 1st of each month from October, 2002 through April, 2003 students will be receiving assignments taken from TRIGONOMETRY;

2. the assignments are supposed to be mailed back to us postmarked no later than the 20th of each month;

3. the graded assignments will be returned to students together with the next assignment by the 1st of the next month.

To enroll to UAB MASC please call UAB Special Studies at (205)934-8263 and mention the UAB Mathematical School by Correspondence (UAB MASC). The tuition is $150. After completing a course, students will receive a Diploma of Completion, but most of all they will have received a deep knowledge of one of the basic mathematical fields.

Contact information:

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about UAB MASC in PDF

Math-by-Mail Contest 2002Math-by-Mail competition is run by the Outreach Program at the Department of Mathematics at UAB since Spring 2001. This is an individual contest presented by our Outreach Program and designed to test logical thinking and depth of understanding of mathematics by high school students. The contest is open to all high school students from participating schools starting at the freshman level.

If you are interested in the problems and in other details concerning UAB Math-by-Mail Contest 2002 you can download all this information in PDF format.

- Information about UAB Math-by-Mail Contest 2002 in PDF

Contact information:

Dr A. Blokh, Coordinator of Outreach Program Department of Mathematics University of Alabama at Birmingham Birmingham, AL 35294-1170 (205)934-2154 ablokh@math.uab.edu |

Train Your Brain Math ClubTrain Your Brain Math Club meets on Fridays at 4:20-5:20pm. The aim is to teach high school students how to solve interesting and often hard but still elementary problems. This should be quite helpful to those of the students who want to succeed in Math Contests such as AMC and ARML.

We use a variety of sources, including the problems from AMC 10 and AMC 12 competitions as well as some other collections of problems. Occasionally, certain topics from more advanced Mathematics (such as elementary Graph Theory, Set Theory or Discrete Mathematics) are considered.

Students who are interested in joining Train Your Brain Math Club should call UAB Special Studies at (205)934-8263 and mention Train Your Brain Math Club.

Contact information:

Dr A. Blokh, Coordinator of Outreach Program

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about Train Your Brain Math Club in PDF

UAB Mathematical School by Correspondence (UAB MASC)The UAB Department of Mathematics and UAB Special Studies announce a new initiative aimed at reaching out to high school students interested in Mathematics.

In the second semester of the academic year 2001-2002 we will run a UAB Mathematical School by Correspondence (UAB MASC). The School is devoted to an in-depth study of Trigonometry. We have chosen this field because it is related to Geometry and Analysis which are major topics in Mathematics. Studying at UAB MASC will allow students to develop a better understanding of these topics and of Mathematics as a whole. The main focus of the School will be on a theoretical study of Trigonometry, and on developing problem-solving skills which can then be applied to all kinds of problems, not necessarily related to Trigonometry. Therefore, studying at UAB MASC could be helpful for preparing for the mathematical part of tests like ACT or SAT.

The main audience of UAB MASC are 10-, 11- and 12-graders, even though as an exception we are willing to consider some 9-graders who have already covered Geometry. The textbook used in the school will be the following:

TRIGONOMETRY

by I. M. Gelfand, Rutgers University, NJ

M. Saul, Bronxville Schools, NY

Birkhauser, Boston-Basel-Berlin, 2001, ISBN 0-8176-3914-4The textbook can be ordered by mail from any major bookseller in the US or can be purchased through a local bookstore. I. M. Gelfand, originally from Moscow, currently from Rutgers University, is one of the greatest living mathematicians who devoted a lot of his time to working with high school students. He organized a very successful Mathematical School by Correspondence which has been operating in Moscow for a long time and in which a number of famous Russian mathematicians studied. UAB MASC is modeled after that school and will function as follows:

1. by the 1st of each month from January through May, 2002 students will be receiving assignments taken from TRIGONOMETRY and other sources;

2. the assignments are supposed to be mailed back to us postmarked no later than the 20th of each month;

3. the graded assignments will be returned to students together with the next assignment by the 1st of the next month.

To enroll to UAB MASC please call UAB Special Studies at (205)934-8263 and mention the UAB Mathematical School by Correspondence (UAB MASC), the course number NR2-5050-10A-02. The tuition is $100. After completing a course, students will receive a Diploma of Completion, but most of all they will have received a deep knowledge of one of the basic mathematical fields.

Contact information:

Dr A. Blokh, Coordinator of Outreach Program

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about UAB MASC in PDF

Train Your Brain Math ClubContact information:

Dr A. Blokh, Coordinator of Outreach Program

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about Train Your Brain Math Club in PDF

Train Your Brain Math ClubContact information:

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about Train Your Brain Math Club in PDF

Contact information:

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.edu

- Information about Train Your Brain Math Club in PDF

Math-by-Mail Contest 2001ELIGIBILITY

Math-by-Mail competition is an individual contest presented by the UAB Department of Mathematics and designed to test logical thinking and depth of understanding of mathematics by high school students. The contest is open to all high school students from participating schools starting at the freshman level.

PRIZES AND CEREMONY

One first prize ($60), one or two second prizes ($40) and 5 third prizes ($20) will be handed out together with award diplomas. All other participants will receive certificates honoring their participation. The school with the best overall performance will be awarded the UAB traveling Math trophy. Prize winners will be invited to an awards ceremony at UAB on Friday May 11th. Parents and teachers will also be invited. The program will feature awards presentation and refreshments.

RULES AND JUDGING.

Math-by-Mail contest is an individual contest. Students must solve problems on their own. All solutions must be self-contained; no references to facts and mathematical results beyond the high school standard curriculum are permitted (nor will they be necessary).

The explanations must be detailed and thorough. Professors of the Department of Mathematics at UAB will judge the entries. Your reasoning process and method of finding the solution will be evaluated. Criteria will include correctness and elegance of solutions. The decision of the judges is final. The entries will not be returned.

FORMAT AND CONTACT INFORMATION

Problems and a cover sheet will be faxed to participating schools on Thursday April 26th, 2001. Every participant must include a copy of the cover sheet; each solution must be written on a separate sheet of paper with the student name and the school name on it. Submit your entry by Tuesday, May 1st to:

UAB Math-by-Mail Contest

Department of Mathematics

UAB, UAB Station

Birmingham AL 35294-1170

Contact information:

Department of Mathematics

University of Alabama at Birmingham

Birmingham, AL 35294-1170

(205)934-2154

ablokh@math.uab.eduUAB MATH-BY-MAIL CONTEST 2001, PROBLEMS

Problem 1. Find all integers n with initial digit 6 which have the following property: if the initial digit is deleted, the resulting integer m is equal to n/25.

Problem 2. We are given 27 coins of the same denomination; we know that one of them is counterfeit and that it is lighter then the others.

1) Locate the counterfeit coin by using three weighings on a pan balance.

2) How many weighings are necessary to solve the same problem with 243 coins and how would you do this?

Problem 3. Point O is given in the plane containing a square ABCD. Prove that the distance from O to one of the vertices of the square is not greater than the sum of the distances from O to the other three vertices.

Problem 4. Every living person has shaken hands with a certain number of other persons. Prove that the number of people who have shaken their hands an odd number of times is even.

Problem 5. Given 5 positive integers, it is known that any four of them can be divided into two groups, two in each group, so that the sum in each group is the same.

1) Show that all these integers are equal.

2) Solve the same problem with 13 integers for which it is known that any 12 of them can be divided in two groups, six in each group, so that the sum in each group is the same.

If you are interested in learning how to solve these problems and in other details concerning UAB Math-by-Mail Contest 2001 (including the names of the winners!) you can download all this information in PDF format.

- Information about UAB Math-by-Mail Contest 2001 in PDF