International Regions Mathematics League (IRML)
Results
May 30, 2009
| IRML 2009 - ONSITE DIVISION | ||||
| Rank | Team | Site | Total | |
| 1 | China Macau | UNLV | 128 | |
| 2 | Columbia | GEOR | 109 | |
| 3 | Philippines | UNLV | 80 | |
| IRML 2009 - CORRESPONDANCE DIVISION | ||||
| Rank | Team | Total | ||
| 1 | HWA Chong Institution | 164 | ||
| 2 | Hong Kong Team A | 160 | ||
| 3 | Vietnam 3 | 130 | ||
| 4 | Surya Institute (Indonesia) | 123 | ||
| 5 | Hong Kong Team B | 108 | ||
| 6 | Istanbul 1 | 106 | ||
| 7 | Vietnam 1 | 101 | ||
| 8 | Vietnam 2 | 98 | ||
| 9 | TED Ankara College Team | 65 | ||
| 10 | Istanbul 2 | 63 | ||
| 11 | St. John's College School | 61 | ||
| 12 | Vietnam 4 | 51 | ||
| 13 | Germany | 48 | ||
| 14 | Istanbul 3 | 46 | ||
| 15 | Istanbul 5 | 37 | ||
| 15 | Istanbul 4 | 37 | ||
| 17 | Istanbul 6 | 24 | ||
An Introduction to IRML:
IRML stands for the International Regions Mathematics League. It is an extension of ARML which stands for the American Regions Mathematics League. ARML began in 1976 as a contest between all-star teams of 15 students each chosen from various regions such as the state of North Carolina, Montgomery County near Baltimore, or New York City. Because these teams have the best students in a region, ARML has always had interesting and challenging problems given in a variety of formats, some of which allow students to work together and some of which are individual in nature. Teams from Canada have been involved from almost the beginning and in the late 1980's ARML invited a team from Moscow to come to the US to participate. That led to teams from Taiwan, the Philippines, and Columbia participating in the States. ARML is an on-site competition. Currently, there are 4 regional sites--Penn State, the University of Georgia, the University of Iowa, and the University of Nevada at Las Vegas. Teams choose which site they want to attend but, of course, they choose the site that is the easiest to get to. Since it is very expensive for international teams to attend, ARML decided to have a competition via the Internet so that international teams could take the contest in their own country. That contest is called IRML. Currently, there are three divisions in the overall contest. One is called ARML and it is between American teams and is taken at one of the four sites. The other two belong to IRML, i.e., IRML has two divisions, one for the international teams that take the contest in America, and the other for international teams that take it in their home country.
The IRML problems are the same as the ARML problems. The ARML contest starts at 8 am Eastern Daylight Time on the first Saturday after Memorial Day in America. In 2009 the contest takes place on Saturday, May 30. We hope that the international teams can take the contest at about the same time as the American teams. For example, Turkey is 7 hours ahead of Penn State, so if Turkey begins at 2 or 3 in the afternoon on Saturday, May 30, then teams from Turkey would be taking the contest more or less at the same time as their American counterparts.
The contest is generally given in English but we have had some success in getting it translated. In 2008 we translated the contest into Chinese, Vietnamese, and Spanish.
Forming a Team:
While it is possible to form a team of 15 from the students of just one school, there are relatively few schools that can form a team that will be successful. So we hope that the organizers of a team will seek out the best students from a region. Generally, that will be the best students in a city or province. Teams in America are chosen in a variety of ways. In Massachusetts, the organizers make up a test similar to the Individual Round to give to the students. It has 20 questions. In other areas students with high scores on the AMC 10 and AMC 12 (the American Mathematics Contest which is given in February) are invited to join the team. A region can form more than one team--it can have an A team (its best students), a B team (the second best students), and so on.
ARML is designed to bring together mathematically talented students and teachers for the common purposes of developing mathematically and creating a community of inspiring friends. That is why we hope that in IRML new communities will be formed in cities and provinces in countries around the world.
IRML needs someone in each country to take charge. Surprisingly, that has sometimes been a student who has heard about the contest and wants to form a team. IRML requires organization and effort, but it is well worth it. Someone must form a team in some way, register, and run practice sessions. To provide practice materials, last year's problems are posted on the ARML website, and ARML has several books of problems from previous contests that can be purchased relatively inexpensively. IRML will require practice. Each round has its own challenges. The rounds are described below and at the end some suggestions are given for organizing practices.
Registration:
To register for IRML, please click here . Note that for the first two years registration is free for IRML teams taking it in their home country. After that we must charge to cover a variety of expenses connected with IRML.
If you have questions about IRML, please contact Don Barry at dbarry@andover.edu or Bryan Sullivan at jbsully@verizon.net.
If you have questions about the registration procedure, please contact Michael Curry at mcurry@arml.com or call 917 495 4961.
Important Information About ARML Contest Procedures:
The proctor(s) should use a stopwatch and should supply plenty of paper. Calculators are not allowed on any part of the contest.
The contest is given in this order:
- The Team Round. The team of 15 gets 20 minutes to solve 10 problems. They can work together but they cannot use calculators. Only the answer is graded. The proctor should pass out a question sheet for each person face down. When everyone has a question paper the proctor says to begin. The proctor announces when 3 minutes are left and when 1 minute is left. The team writes its answers on the answer sheet. When time is called they must stop. Each right answer is worth 5 points so this round is worth 50 points.
- The Power Question. The team gets 60 minutes to solve a series of questions based on one idea. Some problems require just a numerical answer, some problems require proofs. The students work together. Often they divide up the questions and the better students work on the harder questions. Often different groups of students write up the solutions to their part and then all the solutions are put together. In this part the whole solution is graded. Students should show their work when it is called for. The team cannot submit alternate proofs—they must choose one. If they happen to submit alternate proofs all will be graded but the one with the fewest points will count. This question is worth 50 points. Partial credit is given. The proctor gives a 10 minute warning and a 3 minute warning. Calculators are not allowed.
- The Individual Round. On this part the students work separately, no talking is allowed, and no calculators are allowed. The students receive a total of 10 questions in pairs. They have 10 minutes for each pair. Only the answer is graded. After the pair of questions has been passed out face down, the proctor tells the students to turn the questions over. The proctor then reads the question and then says to begin. No work can begin until the proctor finishes the reading and says to begin. We have the problem read to reduce misunderstanding. The proctor gives a 1 minute warning and a 15 second warning. When the proctor says to stop, all work must cease. Only the answer is graded. There is one point per student for each correct answer. With a team of 15 there are 120 points on this round.
- The Relay Round. Each relay round lasts for 6 minutes. The team of 15 is divided into 5 groups of 3. Each group of 3 has a first person, a second person, and a third person. The first person can solve his/her question. The 2nd person needs the first person's answer to solve the problem. The 3rd person needs the 2nd person's answer. Students can only pass answers back. They cannot talk or send any other information. In particular, they cannot send their problem back. Numbers such as 6, 9 18, and 81 can be underlined to show the correct orientation, but otherwise, the slips passed back can contain no additional information. The 3rd person's answer is the only one that is graded.
A student can pass back only one slip of paper at a time, but the student may pass back more than one slip of paper during the relay. For example, if a student gets an answer, passes it back and then redoes the problem and gets a different answer, the student may then pass the new answer back. If the student redoes the problem and gets the same answer, the student may pass the same answer back as a way of telling the next person that the student is confident of that answer.
The proctor passes out the first question to each of the 5 first students, the second question to each of the 5 second students, and the third question to each of the 5 third students. The questions are passed out face down. The proctor then says to begin. At 2 minutes 45 seconds the proctor announces that there are 15 seconds to 3 minutes. At 3 minutes the proctor announces that 3 minutes are up. The students can continue working but the proctor will collect any answers that the third person has to submit. At 5 minutes and 45 seconds the proctor announces that there are 15 seconds left. At 6 minutes the proctor says to stop and the third student submits an answer. A team of 3 may submit an answer at 3 minutes and at 6 minutes. The only answer graded for that team of 3 is the last one submitted. A correct answer at 3 minutes is worth 5 points, a correct answer at 6 minutes is worth 3 points.
Examples: Suppose the correct answer to the 3rd person's problem is 12.- At 3 minutes the 3rd person submits 9 and no answer is submitted at 6 minutes. That team of 3 gets 0 points.
- At 3 minutes the 3rd person submits 12 and no answer is submitted at 6 minutes. That team of 3 gets 5 points.
- At 3 minutes the 3rd person submits 9 and at 6 minutes, the person submits 12. That team of 3 gets 3 points.
- At 3 minutes the 3rd person submits 12 and at 6 minutes, the person submits 9. That team of 3 gets 0 points.
- At 3 minutes the 3rd person submits 12 and at 6 minutes, the person submits 12. That team of 3 gets 3 points. So students should not submit the same answer twice.
- At 3 minutes the 3rd person submits 10034 and at 6 minutes, the person submits 3445. That team of 3 gets 0 points.
There are 25 points possible for each relay so 50 points for both relays.
Additional Notes on Relays:
The second or third person's problem usually starts "Let T = TNYWR". TNYWR is an abbreviation for The Number You Will Receive, so the problem "Let T = TNYWR. Compute (5)(T)" is to be read as "Let T be the number you will receive. Compute 5 times T.
It is important to realize that on the relay races there can be no communication forward. Suppose that the second person's question reads: "Let T = TNYWR. Compute the sum of the interior angles of a T-sided polygon." Person #2 knows that he or she will receive an integer greater than or equal to 3. But suppose person #1 passes back 2/3, clearly the wrong answer. Person #2 can't say anything, groan loudly or softly, or crumple up person #1's answer and throw it on the ground. Person #2 must not give any indication that person #1 made a mistake. Person #1 can, of course, continue to work on the problem and if #1 finds a mistake, #1 can pass back a different answer. Not all is lost if 2/3 is passed back. Person #2 may gamble that the first problem asked for the sum of the numerator and denominator and so guess that T = 5.
It is also important to realize that there is no communication backwards except for the answer. For example, when person #1 passes an answer back, #1 cannot write "I'm not sure" or "I'm positive" or "the answer could be one of 3, 5, or 6" on the slip passed back. Just the answer. Numbers such as 6 or 9 can be underlined to prevent confusion, but other than that nothing can be added to the answer. The second person only passes back his or her answer--the third person does not receive the first person's answer as well. Person #1 can redo the problem and if he/she gets the same answer, he/she can pass that back, and that is a legitimate way of indicating to Person #2 that the answer is thought to be correct.
Not all is lost if person #3 doesn't receive an answer. Suppose that the third problem reads: "Let T = TNYWR. Compute the number of numbers in the following sequence that are divisible by 4: 1, 2, 3, . . . , 45T where T is a digit between 0 and 9." In this case the third person can quickly determine that the answer is either 112, 113, or 114 and can guess one of those if all else fails.
Relay Round Examples:
Click here for a some examples of the Relay Round. An analysis of the rounds is provided at very end of the document.
Submitting Results:
Scores will be submitted using an excel spreadsheet. They will then be sent to two email addresses and one fax number. Click here to download the spreadsheet. When completed, it should be emailed simultaneously to mikecurry@arml.com and chaotia@gmail.com. Then print out and fax the scores to 617 500 0979. Please be sure to apply the United States "country code" when dialing this number. This code is different for each country where the call originates so please check with your phone company for the correct code to use.
A day or so before the contest the proctors will receive all the questions as well as answers to the team, individual, and relay rounds. These must be kept secure. The questions should be run off the day of the contest. The Individual Round question sheet must be cut so that questions are submitted in pairs. The Relay Round question sheet must be cut so that students receive their one problem. No student can see the other problems in the relay.
Team Round: the team round will be graded on site. Each correct problem is worth 5 points. The spreadsheet for submitting the results can be found here. Put a 5 or a 0 under the number of each question on the excel spreadsheet. This information will help us obtain statistics on the difficulty of each question.
Power Question: remember, the team as a whole submits one answer to each question. Do not have each student submit an answer. The Power Question will be graded in the States so fax the solutions to the following number: 617 500 0979. Please be sure to apply the United States "country code" when dialing this number. This code is different for each country where the call originates so please check with your phone company for the correct code to use.
The reason for grading the question in the States is that the authors create a grading rubric prior to the contest. But in the morning of the contest the large group of graders goes over the contest and modifies what will be done. During the actual contest additional changes may be made to the points that are given out. The reason for all this is simple--we simply don't know all the different responses of the students.
Individual Round: student answers will be graded on site. Results will be submitted on the spreadsheet found here. Note that the student names must be listed, last name first, followed by a comma, and then the first name. Note also that under each problem number the student will receive a 1 or a 0.
Relay Round: the third persons' answers will be graded on site. 5 points for a correct answer after 3 minutes and 3 points for a correct answer after 6 minutes. Results should be submitted on the spreadsheet found here. Only the total number of points for each team of 15 on each relay is to be given.
Grading the Answers:
ARML has very strict rules regarding answers. The rules hold for all parts of the contest. For example, suppose the answer to a problem is 4, 5, and 7. If a student or team puts down just 4 and 5, the answer is wrong and they receive a score of 0. If a student or team puts down 4, 5, 7, and 8, the answer is wrong and they receive a score of 0. There is no partial credit given for getting part of the answer correct.
In addition ARML has very strict rules regarding the form of the answer. See ARML specifications below.
Answer Specifications:
These are the same for all 4 rounds. See the conventions sheet for important information regarding acceptable forms of submitted answers. In particular, items 1 and 2 on the conventions sheet describe acceptable forms of the answer.
Additional Parts of the Contest:
ARML has a two other parts. Following the relay races is the 5th part, the Super Relay. It is just for fun and doesn't count in the competition. In this relay, the whole team forms one relay. Person #1 passes to #2 to #3 and so on down to #8. Person #15 passes to #14 to #13 and so on down to #8. So person #8 receives 2 answers and his problem generally requires 2 answers. Since it doesn't count we often have some fun with the Super Relay. For example, it may be that person #2 can, in fact, solve the problem without the answer from person #1. Some students discover this, some don't. Since the IRML teams taking the contest abroad are often doing it late in the afternoon or at night, we haven't been emailing this part of the contest.
The 6th part is the Tiebreaker. This is given to the top students on the individual round who took the contest in the States. At all four sites the best students come down to the front of the auditorium, they are given the problem, told to begin, and each student is timed. Those with the correct answer and the best times are the winners. We aren't giving this to those students who take the contest abroad.
Organizing Practices:
Practice is essential, partly to develop mathematical skills, partly to create a team that works efficiently and effectively. ARML's authors respect the talent of the students taking ARML/IRML so the problems not only cover a variety of topics but include a variety of ways of thinking. Many students discover that they've taken too narrow an approach to problem solving in the past. Studying past ARML problems and taking the contest can truly help students and teachers develop their talent.
The Team Round: students need to learn to make sure that all the problems are being worked on, they need to post answers, they need to post either confirmation of the answer, or a different answer, and if students disagree, they need to work together to come up with a common answer. Before the questions have been passed out, the best teams write the numbers 1 through 10 on the board, leaving space for answers and second opinions. If teams don't do this, they often find that only 1 person did a problem and that person got it wrong. So practice sessions should include sample team rounds of from 5 to 10 questions to give students practice in organizing their work as a group.
The Power Question: it is useful at several practices to do part of a previous Power Question. These should be graded at the site and the results gone over with the students. Many students are not used to doing proofs and often they are dogmatic and don't properly justify their reasoning. They can also see methods that they may know, such as mathematical induction used on problems where they might not have thought to use it. The solutions given to the PQ are more fully developed in many cases than we would expect the students to accomplish.
The Individual Round: at each practice 3 to 4 pairs of individual questions should be given. Typically, in each pair there is an easier problem and a more difficult problem. Often either problem #1 or #9 is the easiest and #10 will be the most difficult. If we hope that 85% of the students will get the first problem correct, we expect that less than 5% will get the last problem correct. Practices will help the students get a feel for the amount of time that they have. Just getting one of the two correct is a good result so students need practice in deciding which problem they have the best shot at. A common mistake is to write the correct answer in the wrong form. Students need to practice to automatically write the answer in the correct form. See the conventions form for a discussion of the right form to use.
The Relay Races: since these are considerably different from other contests, they require a lot of practice. I've attached a sample of 6 relay races with an analysis of each one to show the kind of thinking involved. While these are easier than the regular relays, they still present the kinds of problem solving opportunities that students face when tackling relays.