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21 st Harvard-MIT Mathematics Tournament HMMT February Saturday, February 10, 2018
21st Harvard-MITMathematics Tournament
HMMT February
Saturday, February 10, 2018
February 10, 2018
Hello HMMT community,
W elcome to the 2018 Harvard-MIT February Math Tournament, our21st year running! After months of writing problems, organizing
registration, and developing software, we are thrilled to see all of you inCambridge. Whether you’re joining us from Beijing, Bulgaria, or Boston,we hope you’re as excited as we are!
We at HMMT seek to share our passion for mathematical problem-solving. While math itself remains a core piece in our mission, we seeyear after year that people are just are as important. Many of us helpingto organize HMMT can trace our friendships to events like these, long afterwe have graduated. While we won’t speculate why these events engendersuch lasting bonds, we encourage you to take advantage of this amazingopportunity. Over breakfast, between rounds, and even during our cere-monies, introduce yourself to students from other teams. Say hello to someof our sponsors. And most importantly, thank your coaches and parents. Asscholars, you’re here with over 800 of the brightest, most mathematically-gifted students in the world. Who knows what you will find? As usual,all of our problems have been written and compiled by Harvard and MITundergraduates. No matter how many of them you solve, we hope you findthem both challenging and engaging.
To the coaches, teachers, and parent chaperones: thank you for yourdedication to helping your students compete. We have several talks thatwill be specifically aimed at parents, coaches, and proctors, and we hopeyou find it engaging. There will be a guts round viewing room available aswell.
To help navigate the campus, we have included a map inside the pro-gram and posted signs to direct you around MIT. Moreover, all teams’ roomassignments can be found inside the program. Should you have any ques-tions, comments, or concerns, please don’t hesitate to contact an HMMTstaff member (dressed in pink HMMT shirts) for help.
Whether this is your first or fourth HMMT, we hope that you enjoy thetournament we’ve put together. Good luck today, and above all, have fun!
Regards,
Andrew HeNathanael ChoTournament Directors
Henrik BoeckenAllen LiuKevin SunFebruary Problem Czars
Teams and Room Assignments
Nickname Organization Team Indiv Guts Awards
10101010101 Princeton High School 4-159 10-250 26-100 26-100
A* Air AlphaStar Academy 26-204 26-100 26-100 26-100
A* Earth AlphaStar Academy 26-210 26-100 26-100 26-100
A* Fire AlphaStar Academy 26-302 26-100 26-100 26-100
ABRHS Acton-BoxboroughRegional High School
34-101 34-101 26-100 26-100
Arcana Olympiads School 4-261 32-123 34-101 10-250
AC3 ASDAN China 10-250 10-250 26-100 26-100
AC4 ASDAN China 26-100 10-250 26-100 26-100
BCA Alpha Bergen CountyAcademies
26-100 26-100 26-100 26-100
BCA Mu Bergen CountyAcademies
2-146 26-100 26-100 26-100
BZS Sistema Elite de Ensino 36-144 34-101 34-101 26-100
BS EREM Jos de AlmeidaMaciel
56-167 6-120 34-101 26-100
CMP1 Chesapeake 10-250 10-250 10-250 10-250
CMP2 Chesapeake 26-100 10-250 10-250 10-250
CMP3 Chesapeake 2-131 10-250 10-250 10-250
CHAIR Stevenson High School 4-145 4-370 34-101 26-100
BJSTFX2 China Beijing STFXEducation INC
34-101 34-101 34-101 10-250
CK Lincoln High School 4-265 32-123 26-100 26-100
Daisy The Hockaday School 56-154 6-120 34-101 26-100
DSC DIAMOND STUDYCENTRE
32-123 32-123 10-250 10-250
Eckener Eckener-Gymnasium 36-144 34-101 34-101 10-250
Florida A FLSAM 26-322 26-100 10-250 10-250
Florida B FLSAM 26-100 26-100 10-250 10-250
GNS A Great Neck South HighSchool
34-101 34-101 34-101 10-250
Gunn Beta Gunn High School 32-123 32-123 26-100 26-100
bffls The Harker School 4-145 4-370 34-101 26-100
HMMTB Beijing No4 34-101 34-101 34-101 10-250
Horizon Shenzhen Senior HighSchool
36-112 34-101 34-101 26-100
Hotchkiss Blue The Hotchkiss School 26-314 34-101 34-101 10-250
HSRMU1 Ideamath 32-123 32-123 10-250 10-250
HSRMU2 Ideamath 4-153 32-123 10-250 10-250
Nickname Organization Team Indiv Guts Awards
HSBNU1 Beijing normaluniversity affiliated highschool
34-101 34-101 26-100 26-100
IACS Carmel IACS 2-136 26-100 26-100 26-100
ICAE ICAE 4-265 34-101 34-101 26-100
IMSA Illinois Mathematics andScience Academy
36-112 34-101 34-101 26-100
IT 1 Individuals 10-250 10-250 10-250 10-250
IT 2 Individuals 10-250 10-250 10-250 10-250
IT 3 Individuals 10-250 10-250 10-250 10-250
IT 4 Individuals 10-250 10-250 10-250 10-250
KOREA A KGSEA Korea 10-250 10-250 10-250 10-250
Yeah Knights A WW-P High SchoolNorth
2-139 10-250 10-250 10-250
Yeah Knights B WW-P High SchoolNorth
2-142 10-250 10-250 10-250
KYMA KYMA 4-261 32-123 10-250 10-250
TP Pennon Education 34-101 34-101 34-101 10-250
L’ville The LawrencevilleSchool
34-101 34-101 34-101 10-250
Lehigh Valley F Lehigh Valley 10-250 26-100 26-100 26-100
Ice Lehigh Valley 26-100 26-100 26-100 26-100
Lightning Lehigh Valley 26-204 26-100 26-100 26-100
Lex Alpha Lexington High School 2-147 10-250 26-100 26-100
Lex Beta Lexington High School 2-151 10-250 26-100 26-100
NYCC NYC Math Team 26-210 26-100 26-100 26-100
LC Grays Loomis Chaffee School 4-153 32-123 26-100 26-100
LC Maroons Loomis Chaffee School 32-123 32-123 26-100 26-100
Math Horror Las Cruces PublicSchools
32-123 32-123 10-250 10-250
MN Gold Minnesota All-StateMath Team
2-131 26-100 10-250 10-250
MN Maroon Minnesota All-StateMath Team
26-100 26-100 10-250 10-250
MoCoSwaggaSquad Montgomery Blair HighSchool
26-310 26-100 10-250 10-250
MBHS 2 Montgomery Blair HighSchool
26-100 26-100 10-250 10-250
Moses Brown E Moses Brown School 56-162 6-120 34-101 26-100
NFLS2 Nanjing Foreignlanguage School
2-136 10-250 26-100 26-100
NFLS1 Nanjing Foreignlanguage School
10-250 10-250 26-100 26-100
Nangjing Beijing Math Circle 10-250 10-250 10-250 10-250
Nickname Organization Team Indiv Guts Awards
NCSSM NCSSM 2-139 26-100 10-250 10-250
New Haven New Haven Math Circle 26-322 34-101 34-101 26-100
OCMC Orange County MathCircle
2-143 26-100 10-250 10-250
PEARL Phillips Exeter Academy 26-100 26-100 26-100 26-100
Andover 1778 Phillips Academy 2-132 26-100 26-100 26-100
Andover 2018 Phillips Academy 26-100 26-100 26-100 26-100
Pirates A WW-P High SchoolSouth
10-250 10-250 26-100 26-100
Pirates B WW-P High SchoolSouth
2-132 10-250 26-100 26-100
qwerty137 Amador Valley HighSchool
4-159 32-123 26-100 26-100
RVMT - 1 Raritan Valley MathTeam
4-265 34-101 26-100 26-100
Knights Salisbury School 36-112 34-101 34-101 10-250
SAN1 San Diego 2-147 10-250 10-250 10-250
SAN2 San Diego 2-151 10-250 10-250 10-250
NYCA NYC Math Team 2-142 26-100 26-100 26-100
SFLS SUN Shanghai ForeignLanguage School
4-153 4-370 34-101 26-100
Sharon Sharon Public Schools 4-265 34-101 34-101 10-250
SZZX Shenzhen Middle School 56-154 6-120 34-101 10-250
SixHighsGrow The Association of SixHigh Schools of China
32-123 32-123 10-250 10-250
SixHihgsEver The Association of SixHigh Schools of China
4-153 32-123 10-250 10-250
SMG ”High School ofMathematics ””Dr.Petar Beron”””
2-146 10-250 26-100 26-100
SMMath St. Mark’s School ofTexas
4-261 32-123 26-100 26-100
SLI Star League - Irvine 4-145 4-370 34-101 26-100
Braves Syosset High School 56-154 6-120 34-101 10-250
Team Tennessee Ravenwood HS 26-100 26-100 10-250 10-250
Horned Toads North Houston Academy 26-142 26-100 10-250 10-250
Texas Lobos North Houston Academy 26-100 26-100 10-250 10-250
Javelinas Ivyclimbers Math Team 4-159 32-123 10-250 10-250
RDF ICC Beijing Math Circle 2-135 10-250 10-250 10-250
Foxes The Roxbury LatinSchool
56-162 6-120 34-101 26-100
NYCB NYC Math Team 26-100 26-100 26-100 26-100
Nickname Organization Team Indiv Guts Awards
TJA Thomas Jefferson HighSchool for Science andTechnology
26-314 26-100 26-100 26-100
TJB Thomas Jefferson HighSchool for Science andTechnology
26-100 26-100 26-100 26-100
TJC Thomas Jefferson HighSchool for Science andTechnology
26-142 26-100 26-100 26-100
TSHS Team 1 TSINGHUA UniversityHigh School
32-123 32-123 26-100 26-100
TSHS Team 2 TSINGHUA UniversityHigh School
4-153 32-123 26-100 26-100
TT! TT Math School 34-101 34-101 26-100 26-100
VarBurg ”High School ofMathematics ””Dr.Petar Beron”””
2-143 10-250 26-100 26-100
Washington Gold Washington Gold 2-135 26-100 10-250 10-250
WAA Westchester area alpha 56-167 6-120 34-101 26-100
WMA All Stars Western Mass ARML 26-310 26-100 26-100 26-100
WMASuns Western Mass ARML 26-302 26-100 26-100 26-100
Yu’s Feb A Team Yu’s Elite Education 4-159 32-123 26-100 26-100
ZhichengGo Beijing Zhicheng 4-145 4-370 34-101 26-100
Student Schedule
Friday, February 9, 2018 (Harvard)
Time Event Location
7:00PM – 8:00PM Early registration Science Center 112
7:00PM – 7:45PM Pizza and Ice Cream Science Center Lobby
7:45PM – 8:00PM Mini-Events Preview Science Center Lobby
8:00PM – 9:00PM Mini-Events Science Center Lobby
Saturday, February 10, 2018 (MIT)
Time Event Location
7:30AM – 8:30AM Registration W20 Lobdell
7:30AM – 8:45AM Breakfast W20 Stratton Lounge
8:30AM – 9:00AM Individual CompetitorMeeting
W20 407
9:00AM – 10:00AM Team Round Varies
10:15AM – 11:15AM Algebra Round Varies
11:20AM – 12:20AM Geometry Round Varies
12:25AM – 1:25AM Combinatorics Round Varies
1:30PM – 2:45PM Lunch Forbes Cafe (Bldg 32)
3:00PM – 4:30PM Guts Round Varies
4:30PM – 4:50PM Integration Bee Finals 10-250
4:50PM – 5:30PM Awards Varies
Coaches, Proctors, and Parents Schedule
Friday, February 9, 2018 (Harvard)
Time Event Location
7:00PM – 8:00PM Early registration Science Center 112
7:00PM – 7:45PM Pizza and Ice Cream Science Center Lobby
7:45PM – 8:00PM Mini-Events Preview Science Center Lobby
8:00PM – 9:00PM Mini-Events Science Center Lobby
Saturday, February 10, 2018 (MIT)
Time Event Location
7:30AM – 8:30AM Registration W20 Lobdell
7:30AM – 8:45AM Breakfast W20 Stratton Lounge
8:30AM – 9:00AM Proctor Meeting 2-190
9:00AM – 10:00AM Team Round Varies
10:30AM – 11:30AM HMMT Staff Panel 2-190
1:30PM – 2:45PM Lunch Forbes Cafe (Bldg 32)
3:00PM – 4:30PM Guts Viewing Varies
4:30PM – 4:50PM Integration Bee Finals 10-250
4:50PM – 5:30PM Awards Varies
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 graphpaper, rulers, protractors, compasses, architectural tools, or any otherdrawing aids. Translators are 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 nofractions and 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,s/he must go to the designated Appeals Room and submit an appeal inwriting. The deadline to do so will be announced on the day of the contest.Decisions of the coordinators of the February Harvard-MIT MathTournament are final.
Local Information
Lodging
• Le Meridien Cambridge-MIT20 Sidney Street, Cambridge, MA 02139(617)-577-0200
• The Kendall Hotel350 Main Street, Cambridge, MA 02142(617)-577-1300
• Boston Marriott Cambridge50 Broadway, Cambridge, MA 02142(617)-494-6600
Food
Kendall Square
• Au Bon Pain238 Main Street
• Chipotle Grill2 Cambridge Center
• Panda Express3 Cambridge Center
• Clover (all vegetarian)5 Cambridge Center
• Sebastians415 Main Street
MIT Student Center (W20)
• Anna’s TaqueriaFirst floor
• Dunkin’ Donuts/Cambridge GrillFirst floor
• Lobdell Food CourtSecond floor
– Cafe Spice
– Shawarma Shack
– Shinkansen Japan Fast Food
– Subway
Emergency
In the event of fire or life-threatening emergency, call (617) 253-1212 insteadof 911. This number will reach the MIT Police Department.
HMMT Officers and Staff
Officer Team
Tournament Directors: Nathanael Cho, Andrew He
Problem Czars (November): Ashwin Sah, Michael Tang, Yannick Yao
Problem Czars (February): Henrik Boecken, Allen Liu, Kevin Sun
Finance Directors: Emily Cheng, Ellen Li
Registration Directors: Zachary Diamandis, Lillian Zhang
Schedule Coordinators: Cynthia Liu, Grace Whitney
Scripts Director: Yang Liu
Scripts Team: Roger Jin, Ashley Kim, Alexander Wei
Webmaster: Grace Zhang
Outreach Chairs: Brice Huang, Ahaan Rungta
Social Chair: Celine Liang
General Officer: Emery Liu
Special Projects Directors: Michelle Chen, Jakob Weisblat
Historian: Evan Chen
Staff Members
Assistant Historian: David Liang
Brochure Coordinator: Sarah Wu
Building Coordinators: Jane Ahn, Andres Fabrega, Natalia Hajlasz, Luke Melas-Kyriazi, Francisco Proskauer, Cindy Yang
Driver: William Qian
Finance Associates: Anurag Golla, Isabella Kang, Kim Nguyen, Rebecca Shin
Food Czars: Xiaolu Guo, Ting Li
Guts Round Directors: Karen Chen, Daniel Qu, Sophia Xia
Head Graders: Mark Kong, Nelson Niu, Aaditya Singh
Head Proctor: Matthew Hambacher
Logistics Coordinators: Sambuddha Chattopadhyay, Aditi Chitkara, William Ho
Problem Committee: Varkey Alumootil, Kevin Chen, Daniel Chiu, Angela Deng,Sanath Devalapurkar, Johnny Gao, Caleb He, Cory Hixson, Serina Hu, Dhaman-preet Kaur, Sujay Kazi, Mendel Keller, Michael Kural, Jason Lu, Faraz Masroor,Gabriel Mintzer, Junyao Peng, Saranesh Prembabu, Qi Qi, Chad Qian, NikhilReddy, Dhruv Rohatgi, Mehtaab Sawhney, Christopher Shao, Quilee Simeon,Alec Sun, Amanda Wang, Nathan Weckwerth, Farrell Wu, John Wu, David Xi-ang, Christopher Xu, Calvin Yost-Wolff, Kevin Yang, Rachel Zhang, Fan Zhou,
Photographers: Steven Hao, Vivian Huang, Abraham Park, Joyce Tian
Prize Czars: Anton Cao, Baula Xu, Byron Xu
Sign Czars: Christina Chen, Kenz Kallal, Ben Nguyen
Spokespersons: Paolo Adajar, Rogers Epstein, Vaughan McDonald, Hadrian Merced,
Cathy Wang, Michael Xie, Thomas Xiong, Justin Yu
Sponsors
Special thanks to our sponsors:
21st Harvard-MIT Mathematics TournamentFebruary Tournament 2018
