23rd harvard-mit · columbia math circle 10-250 1-135 10-250 bzsbra eleva educacao 34-101 4-159...
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23rd Harvard-MITMathematics Tournament
HMMT February TournamentSaturday, February 15, 2020
February 15, 2020
Hello HMMT 2020 February Contestants!
T he HMMT organizing team is delighted to have you join us here in Cam-bridge! We have all been committed to building this February’s competition
into an experience that we hope you will recall fondly for many years to come.
These couple of days every year are truly special for us, and we hope that youall will find the same statement holds for you. As we celebrate the wonderfuldiscipline of math by contest, do not forget that even more importantly, we gatherhere to showcase your mathematical achievement.
Those of you who are seasoned veterans of HMMT may recall that our previoustournament directors have equated the importance of the human element ofHMMT to that of math. This year, we take this statement further; the humanelement of HMMT is crucial to our competition. Take the time to speak to theother incredibly bright students around you, but more importantly, listen. Wehope that you will find remarkable in getting to know your exceptional peers.
To the coaches, parents, and chaperones: we have seen how much you care aboutgranting your students opportunities to pursue their interests, and we cannotexpress enough how appreciative we are for your support of the next generationof mathletes. Through the toils of registration, the anxiety of the lottery, and thelogistical taxes of organizing the trip here, your commitment shines.
As you navigate MIT’s campus, we hope you will find the map in this brochurehelpful. Please check your team’s room assignments carefully and notify anyHMMT member if you require any assistance. We understand that the campuscan be hard to navigate at first, and we’re here to help!
Once again, we are excited to have you join us for today’s tournament, and wewish you all the best in the competition!
Regards,
Jeffery YuWilliam HoTournament Directors
Evan ChenWilliam QianChief Advisors
Andrew GuJames LinMichael RenFebruary Problem Czars
Student Schedule
Friday, February 14, 2020 (Harvard)
6:30PM 8:00PM Early Registration Science Center
6:30PM 7:15PM Pizza and Ice Cream Science Center
7:15PM 7:30PM Mini-Events Preview Science Center
7:30PM 9:00PM Mini-Events Science Center
Saturday, February 15, 2020 (MIT)
7:30AM 8:30AM Breakfast W20 (Student Center)
7:30AM 8:30AM Registration W20 La Sala (W20-202)
8:15AM 8:45AM Individual CompetitorMeeting
W20 West Lounge(W20-201)
9:00AM 10:15AM Team Round varies
10:30AM 11:30AM Algebra Round varies
11:40AM 12:40PM Geometry Round varies
12:50PM 1:50PM Combo Round varies
1:50PM 3:00PM Lunch W20 (Student Center)
3:00PM 4:45PM Guts Round 10-250, 26-100, 34-101
5:10PM 5:35PM Integration Bee Finals Kresge Auditorium
5:45PM 6:30PM Awards Ceremony Kresge Auditorium
Sunday, February 16, 2020 (MIT)
8:00AM 8:45AM Breakfast 1-190
8:00AM 8:45AM Registration 1-190
9:05AM 9:55AM Class Block 1 varies
10:05AM 10:55AM Class Block 2 varies
11:05AM 11:55AM Class Block 3 varies
12:00PM 1:00PM Lunch on own
1:05PM 2:25PM Class Block 4* varies
* Some classes may end at 1:55PM.
Coach, Proctor, and Parent Schedule
Friday, February 14, 2020 (Harvard)
6;30PM 8:00PM Early Registration Science Center
6:30PM 7:15PM Pizza and Ice Cream Science Center
7:15PM 7:30PM Mini-Events Preview Science Center
7:30PM 9:00PM Mini-Events Science Center
Saturday, February 15, 2020 (MIT)
7:30AM 8:30AM Breakfast W20 (Student Center)
7:30AM 8:30AM Registration W20 La Sala (W20-202)
8:10AM 8:40AM Proctor Meeting W20 Twenty Chimneys(W20-301)
9:00AM 10:15AM Team Round varies
12:30PM 1:30PM Student Panel 2-105
1:50PM 3:00PM Lunch W20 (Student Center)
3:00PM 4:45PM Guts Round Viewing 6-120
5:10PM 5:35PM Integration Bee Finals Kresge Auditorium
5:45PM 6:30PM Awards Ceremony Kresge Auditorium
Sunday, February 16, 2020 (MIT)
8:00AM 8:45AM Breakfast 1-190
8:00AM 8:45AM Registration 1-190
9:05AM 9:55AM Class Block 1 varies
10:05AM 10:55AM Class Block 2 varies
11:05AM 11:55AM Class Block 3 varies
12:00PM 1:00PM Lunch on own
1:05PM 2:25PM Class Block 4* varies
* Some classes may end at 1:55PM.
A help center is located in W20-201.
Teams and Room Assignments
Team Name Organization Indiv. Team Guts
AB Red Duck ABRHS 6-120 1-132 10-250
AlphaStar AIR AlphaStar Academy 6-120 5-134 26-100
AlphaStar EARTH AlphaStar Academy 10-250 6-120 10-250
AlphaStar FIRE AlphaStar Academy 32-123 2-190 34-101
BISV Bobcats Basis Independent Silicon Valley 34-101 34-101 34-101
gaosi Beijing AMC Club 10-250 10-250 10-250
BCA 1 Bergen County Academies 10-250 1-134 10-250
BCA 2 Bergen County Academies 26-100 4-149 26-100
BCA 3 Bergen County Academies 32-123 4-153 34-101
BUA Team A Boston University Academy 10-250 1-273 10-250
BUA Team B Boston University Academy 26-100 26-100 26-100
Brewster Team A Brewster Academy 34-101 34-101 34-101
Carleton U Carleton University 26-100 26-100 26-100
NoCoastBestCoast ChicagoHMMT2020 26-100 2-151 26-100
Wild Boars Choate Rosemary Hall 34-101 26-100 34-101
Mile High Mathematicians Colorado Math Circle 32-123 32-123 10-250
CMCA Columbia Math Circle 10-250 1-135 10-250
BZSBRA Eleva Educacao 34-101 4-159 34-101
FALCON EREM Escritor José de Alencar 34-101 34-101 34-101
PEARL Exeter Math Club 26-100 26-100 26-100
Team Name Organization Indiv. Team Guts
Finger Lakes Math Team Finger Lakes Math Team 32-123 32-123 34-101
Florida A Florida Student Association of Mathematics 26-100 2-142 26-100
Florida B Florida Student Association of Mathematics 10-250 2-143 10-250
GV Math Team Garnet Valley High School 10-250 10-250 10-250
Omega Harker School 34-101 34-101 34-101
Indiana Cornstars IACS 26-100 26-100 26-100
Illinois Mathematics and ScienceAcademy Illinois Mathematics and Science Academy 10-250 10-250 10-250
Individuals 1 Individuals 4-163 4-163 26-100
Individuals 2 Individuals 4-163 4-163 26-100
Individuals 3 Individuals 4-163 4-163 26-100
ICAE Indus Center for Academic Excellence 34-101 34-101 34-101
KMLA MSZD Korea Minjok Leadership Academy 10-250 32-123 10-250
SPPS Mathletes Korea Youth Math Association 10-250 10-250 10-250
KYMA Korea Youth Math Association 26-100 26-100 26-100
Korea B Korean Gifted Students Evaluation Association (KGSEA) 10-250 10-250 10-250
LV Fire Lehigh Valley 26-100 3-270 26-100
LV Ice Lehigh Valley 10-250 6-120 10-250
Lex Alpha Lexington High School 26-100 6-120 26-100
Lex Beta Lexington High School 32-123 2-190 34-101
Chesapeake A Metro Maryland Math Circle 26-100 2-146 26-100
Chesapeake B Metro Maryland Math Circle 10-250 2-147 10-250
Team Name Organization Indiv. Team Guts
MI-ALL-STARS Michigan All Stars 26-100 2-136 26-100
MN Gold Minnesota State High School Math League 6-120 2-139 26-100
Texas Momentum A Momentum Learning 26-100 26-100 26-100
MoCoSwaggaSquad Montgomery Blair High School 26-100 5-217 26-100
Blair Beavers Montgomery Blair High School 10-250 1-150 10-250
MVRCS Team 2A Mystic Valley Regional Charter School 32-123 1-277 10-250
NCSSM NC School of Science & Math 26-100 26-100 26-100
New Haven Math Circle New Haven Math Circle 32-123 32-123 10-250
Newton South Newton South Math Team 32-123 1-150 10-250
North Georgia North Georgia 34-101 1-379 34-101
Tin Man NYC Math Team 26-100 2-190 26-100
Scarecrow NYC Math Team 6-120 2-132 10-250
Lion NYC Math Team 32-123 2-135 34-101
Arcana Olympiads School 26-100 4-153 26-100
OMC Ontario Math Circles 10-250 10-250 10-250
OCMC A Orange County Math Circle 10-250 10-250 10-250
OCMC B Orange County Math Circle 26-100 26-100 26-100
Andover 1778 Phillips Academy 6-120 4-253 26-100
Andover 2020 Phillips Academy 10-250 3-270 10-250
Pleasanton Math Team A Pleasanton Math Team 10-250 1-242 10-250
Pleasanton Math Team B Pleasanton Math Team 26-100 26-100 26-100
Team Name Organization Indiv. Team Guts
PHS Math Team Princeton High School 26-100 4-145 26-100
RVMT - Euler Raritan Valley Math Group 32-123 4-231 34-101
SalisburyKnights Salisbury School 34-101 4-237 34-101
SDA1 San Diego 10-250 2-131 10-250
SDA2 San Diego 26-100 26-100 26-100
SMG Sofia High School of Mathematic " Paisii Hilendarski" 26-100 4-144 26-100
St. Mark’s Texas St. Mark’s School of Texas 34-101 34-101 34-101
Steve and Son Steve and Son 34-101 4-261 34-101
We tried ;-; Syosset High School 34-101 34-101 34-101
Hotchkiss Blue The Hotchkiss School 26-100 3-133 26-100
TJA Thomas Je�erson High School for Science and Technology 26-100 4-146 26-100
TJB Thomas Je�erson High School for Science and Technology 6-120 4-265 10-250
TJC Thomas Je�erson High School for Science and Technology 32-123 10-250 34-101
Trident Amazing Trident Academy 10-250 1-136 10-250
UTS A University of Toronto Schools 34-101 3-270 34-101
Washington Gold Washington Gold 26-100 6-120 26-100
Yeah Knights A West Windsor-Plainsboro High School North 26-100 4-149 26-100
Yeah Knights B West Windsor-Plainsboro High School North 10-250 10-250 10-250
Pirates A West Windsor-Plainsboro High School South 10-250 10-250 10-250
Pirates B West Windsor-Plainsboro High School South 26-100 3-270 26-100
WAA Westchester Area Alpha 32-123 32-123 34-101
Team Name Organization Indiv. Team Guts
WMA Stars Western Mass ARML 6-120 6-120 26-100
WMA Suns Western Mass ARML 32-123 32-123 10-250
WMA Moons Western Mass ARML 10-250 2-190 10-250
PHO Westview High School 6-120 26-100 26-100
Wilmington Math A Wilmington High School 32-123 32-123 10-250
Youth EUCLID Youth EUCLID Association 26-100 32-123 26-100
Test Information
Rules
You may not use books, notes, calculators, pocket organizers, slide-rules, abaci,or any other computational aids. Similarly, you may not use graph paper, rulers,protractors, compasses, architectural tools, or any other drawing aids. Translatorsare also prohibited.
Guidelines for Acceptable Answers
• Answers must be simplified and exact unless otherwise specified.
• Rational numbers should be given in lowest terms.
• An nth root should be simplified so that the radicand contains no fractionsand is not divisible by the nth power of any prime.
• Denominators do not need to be rationalized.
• Correct mathematical notation must be used.
• No partial credit will be given unless otherwise specified.
Protests
If a student believes that an answer given on the answer key is incorrect, they mustgo to the designated Appeals Room and submit an appeal in writing. The deadlineto do so will be announced on the day of the contest.
Decisions of the February HMMT coordinators are final.
Rules of Conduct and Expectations for HMMTAttendees
HMMT is organized by undergraduate students at Harvard and MIT under theeponymous student organization at MIT and the Harvard Undergraduate Math-ematics Association. While we receive support from both universities, HMMT isa distinct entity. When you attend our competition, you are a HMMT-sponsoredvisitor to the campuses of Harvard and MIT. As such, we mandate that HMMT at-tendees abide by the following rules of conduct. We strongly urge the coach ofeach organization to carefully read this document and ensure that students arealso familiar with it.
Conduct
While you are an attendee of HMMT, you must abide by these rules:
• Be respectful of people. Rude behavior, inappropriate language, and threatsagainst another person of any nature, whether verbal or physical, executedor suggested, will not be tolerated.
• Dishonesty accompanied by ill intent (including, but not limited to, lying,cheating, doping, and scamming) is forbidden.
• Be respectful of the spaces. While attending the events of HMMT, you are avisitor to the private property of Harvard or MIT. Do not deface the rooms.
• Do NOT eat or drink in classrooms unless designated for eating. Do notdispose of food scraps in classroom waste containers.
• Do not transfer furniture between rooms. If you require more furniture, alerta HMMT o�cer, and arrangements will be made for you.
• Do not linger around doors and stairs or obstruct hallways; please wait inopen locations or your assigned rooms.
• Be responsible for your organization’s members. Penalties may be leveragedagainst an entire organization based on a single person’s actions.
Consequences
The HMMT Tournament Directors reserve the right to disqualify any team at anytime for any reason. In severe situations of misconduct, you may be escorted o� thepremises. Your test results will be nullified, and you will be disqualified. Permanentbans will be imposed upon organizations that severely infringe upon the code ofconduct.
Local Information
Food
• Clover ($)Vegetarian sandwiches andplates.
5 Cambridge CenterCambridge, MA 02139
• Chipotle ($)Mexican fast casual food,including custom-made tacosand burritos.
255 Main St.Cambridge, MA 02142
• Oath ($$)Small local chain withbuild-your-own gourmet pizza.
181 Massachusetts Ave #1Cambridge, MA 02139
• Saloniki ($)Customizable Greek plates,pitas & more.
181 Massachusetts Ave #2Cambridge, MA 02139
• Anna’s Taqueria ($)Local counter-serve Mexicanchain with burritos, tacos &quesadillas.
84 Massachusetts AveCambridge, MA 02139
• Lobdell Food Court ($)Features fast-food options suchas Cafe Spice, ShawarmaShack, and Shinkansen Japan.
84 Massachusetts AveCambridge, MA 02139
EmergencyIn the event of fire or life-threatening emergency, call (617) 253-1212, not 911. Thisnumber will reach the MIT Police Department; they will respond faster than 911.
Harassment PolicyHMMT strictly does not tolerate harassment or violence of any form to our com-petitors and sta�, regardless of the identity of the o�ender. If you believe that youor your competitors have been harassed, please immediately call the MIT PoliceDepartment at (617) 253-1212. If you do not feel comfortable contacting police your-self, please visit the help center in W20-201 and request help with your incident,and we will make every e�ort to help you decide on an appropriate response andrecourse.
SponsorsSpecial thanks to our sponsors:
HMMT O�cers and Sta�
O�cer TeamTournament Directors
• Je�ery Yu• William Ho
Chief Advisors• Evan Chen• William Qian
Community Coordinators• Assel Ismoldayeva• Junu Lee
Education Chair• Agustin Garcia
Finance Directors• Aileen Ma• Christine Cai
Friday Night Events Chair• Andrew Lin
Inventory Czar• Katherine Xiong
Problem Czars (November)• Carl Schildkraut• Krit Boonsiriseth• Milan Haiman
Problem Czars (February)• Andrew Gu• James Lin• Michael Ren
Publicity Chair• Jason Chen
Schedule Coordinators• Lauren Oh• Richard Allen
Software Team• Dennis Giese• Mark Kong• Yannick Yao
Tournament Directors Emeritus• Emery Liu• Lillian Zhang
Sta� MembersAssistants to theTournament Directors
• Aaditya Singh• Ted Pyne
Brochure Coordinator• Ivy Mao
Chief Proctors• Andrew Wu• April Chen• Carolyn Ge• Haneul Shin• Jason Lee• Tristan Shin• Richard Luo
Education Sta�• Melinda Sun• Merrick Cai• Vincent Pan
Finance Associates• Allen Chen• Lucy He• Lucy Jiao
Food Czars• Clara Shi• Hee Jae Hong
Friday Night Assistants• Emma Qin• Vincent Huang
Language/Online Coordinator• Kristy Chang
Membership Deputies• Benji Kan• Matthew Ho
Photographers• Alison Chen• Arun Wongprommoon
Prize Czar• Alison Fang
Problem Captains• Dain Kim• Daniel Zhu• Joshua Lee• Ryan Kim• Sheldon Tan• Shengtong Zhang• Sujay Kazi• Wanlin Li
Problem Editors• Ahmed Zawad Chowdhury• Alan Peng• Alec Sun• Anders Olsen• Anqi Li• Benjamin Qi• Catherine Wu• Chad Qian• Dylan Liu
Problem Editors (continued)• Freddie Zhao• Guanpeng Xu• Hahn Lheem• Handong Wang• Je�ery Li• Joseph Heerens• Katherine Cheng• Kevin Ren• Nurullah Giray Kuru• Sean Anderson Ty• Siva Muthupalaniappan• Siwakorn Fuangkawinsombut• Vincent Bian
Registration Associates• Catherine Mei• Priya Ganesh• Sanjana Ramrajvel
Room Czars• Allen Wang• Amber Li• Austin Li• Brian Tobin• Hanna Yang• Raluca Vlad
Software Team• Aaron Sun• Sophia Zhi• Wendy Wu
T-shirt Designer• Raphi Kang
Map also at http://whereis.mit.edu
23rd Harvard-MIT Mathematics TournamentFebruary 2020