21st harvard-mit mathematics tournament · pdf filersm rsm sc d sv 206 sc d sc a sagerhmmt...

21st Harvard-MITMathematics Tournament

HMMT November

Saturday, November 11, 2017

November 11, 2017

Hello HMMT community,

W elcome to the 2017 Harvard-MIT November Math Tournament,our 21st 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 Shanghai, Tegucigalpa, orBoston, 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 in the Science Center lobby. And most importantly, thankyour coaches and parents. As scholars, you’re here with over 800 of thebrightest, most mathematically-gifted students in the world. Who knowswhat you will find? As usual, all of our problems have been written andcompiled by Harvard and MIT undergraduates. No matter how many ofthem you solve, we hope you find them both challenging and engaging.

To the coaches, teachers, and parent chaperones: thank you for yourdedication to helping your students compete. We have a talk by Po-ShenLoh that will be specifically aimed at parents, coaches, and proctors, andwe hope you find it engaging. There will be a guts round viewing roomavailable as well.

To help navigate the campus, we have included a map inside the pro-gram and posted signs to direct you around Harvard. Moreover, all teams’room assignments can be found inside the program. Should you have anyquestions, comments, or concerns, please don’t hesitate to ask 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

Ashwin SahMichael TangYannick YaoNovember Problem Czars

Teams and Room Assignments

Building Codes: YC Aud. = Yenching Auditorium, SC = ScienceCenter, Sv = Sever

Nickname Organization Indiv. Team Guts Awards

ACM ACM SC 309 SC 309 SC D SC C

Stevenson Adlai E. StevensonHigh School

SC 310 SC 310 SC E SC C

AAMC Cards Albany Area MathCircle

SC C SC C SC C SC C

AHS Albemarle HighSchool

YC Aud. YC Aud. SC B SC B

Almaty 1 Almaty SC E Sv 214 SC D SC C

ASFG american schoolfoundation ofguadalajara


AMSA1 AMSA CharterSchool

SC D SC D SC C SC C

AMSA2 AMSA CharterSchool

SC D Sv 112 SC C SC C

Warriors Andover High School SC E SC E SC D SC B

Austin Math Austin Math Circle SC B10 SC B10 SC D SC B

Beijing BDF Beijing Math Circle YC Aud. Sv 209 SC B SC B

Team De Belmont High School SC 309 SC 309 SC D SC C

BCA 1 Bergen CountyAcademies

SC B SC B SC A SC A


SC B Sv 103 SC A SC A



Bucky Buckingham Browne& Nichols School

SC C SC C SC B SC B

Dayz Buckingham Browne& Nichols School

SC C SC B SC B SC B

CATS Cheshire Academy YC Aud. Sv 210 SC B SC B

Seq Chicago ChicagolandCorollaries


Comm A CommonwealthSchool

SC C SC C SC C SC C

Comm B CommonwealthSchool

SC C Sv 111 SC C SC C

CA1 Concord Academy SC D SC D SC B SC B

CA2 Concord Academy SC D Sv 202 SC B SC B



Chen One Concord CarlisleHigh School

SC D SC D SC C SC C

Smurfs Concord CarlisleHigh School

SC D Sv 203 SC C SC C

CASLV FalconsA

Coral Academy ofScience Las Vegas

SC B10 SC B10 SC E SC B

GMinor Deerfield Academy SC D Sv 201 SC B SC B

Green Deerfield Academy SC D SC D SC B SC B

EB Circle East Brunswick HighSchool

SC C SC C SC C SC C

EB Square East Brunswick HighSchool

SC C Sv 109 SC C SC C

Jesters Emma WillardSchool


FMC Fairfax Math Circle SC 222 SC 222 SC E SC C

GVMathClub Garnet Valley HighSchool

SC B SC B SC B SC B

Gauss Math Gauss Academy ofMathematicalEducation


Gauss Tiger Gauss Math Circle SC B Sv 206 SC B SC B

MKS High TechnologyHigh School

SC A Sv 213 SC D SC B

ICAE1 ICAE SC C SC C SC B SC B

ICAE2 ICAE SC C Sv 110 SC B SC B

IM-1 Ideamath SC D SC D SC B SC B

IM-2 Ideamath SC D Sv 203 SC B SC B

Individual 1 Individuals SC A SC A SC C SC C




KentCT Kent School YC Aud. Sv 211 SC B SC B

Kents Kents Hill School YC Aud. Sv 210 SC C SC C

KGV King George VSchool

SC E Sv 214 SC D SC B

LVMC-A Las Vegas MathCircle

SC B Sv 207 SC C SC C

LVMC-A2 Las Vegas MathCircle

SC B SC B SC C SC C



LCA1 Lexington ChristianAcademy

SC 221 SC 221 SC E SC C

Lex Delta Lexington HighSchool


Lex Epsilon Lexington HighSchool

SC B SC B SC A SC A

Lex Gamma Lexington HighSchool


Big L Club Livingston HighSchool Math Team

SC C Sv 110 SC D SC A

Little L Club Livingston HighSchool Math Team

SC C SC C SC D SC A

LAMC A Louisiana MathCircle

SC C SC C SC A SC A

LAMC B Louisiana MathCircle

SC C SC B SC A SC A

LAMC C Louisiana MathCircle

SC C Sv 107 SC A SC A

ML Martin Luther HighSchool

SC B10 SC B10 SC D SC C

Golden Eagles Middlesex CountyAcademy

YC Aud. Sv 208 SC C SC C

MWM Midwest Math Circle SC E Sv 214 SC D SC C

(H)(MMT) Milton Academy SC C Sv 106 SC C SC C

H(a)MMT Milton Academy SC C SC C SC C SC C

H(y)MMT Milton Academy SC C SC B SC C SC C

MBHS 1 Montgomery BlairHigh School

SC C SC C SC A SC A

MBHS Two Montgomery BlairHigh School

SC C SC B SC A SC A

Moses Brown A Moses Brown School SC D Sv 206 SC B SC B

Moses Brown B Moses Brown School SC D Sv 207 SC B SC B

T1 Mystic ValleyRegional CharterSchool (MVRCS)

SC 222 SC 222 SC E SC B

NNHS-C Naperville NorthHigh School

SC B SC B SC C SC C

NNHS+C Naperville NorthHigh School


Algebros Nashoba RegionalHigh School

SC 309 SC 309 SC D SC B



NNHS Tigers Newton North HighSchool

SC A Sv 213 SC D SC C

Fermat Newton south SC B Sv 208 SC A SC A

NHSMT 1 NH State MathTeam

SC C SC C SC B SC B


SC C SC B SC B SC B


SC C Sv 106 SC B SC B

North Georgia A North Georgia A SC B Sv 209 SC B SC B

Jeju North LondonCollegiate SchoolJeju

YC Aud. Sv 208 SC B SC B

NHS A Northview HighSchool


OH Ohio ARML SC B Sv 112 SC B SC B

Andover A1 Phillips Academy SC B Sv 106 SC C SC C

Andover A2 Phillips Academy SC B SC B SC C SC C

Andover A3 Phillips Academy SC B Sv 102 SC C SC C

PEA IdeaMathCi

Phillips ExeterAcademy

SC B Sv 103 SC B SC B

PEA IdeaMathUn

Phillips ExeterAcademy


PEAK Phillips ExeterAcademy


PEAR Phillips ExeterAcademy

SC B SC B SC B SC B

PEAT Phillips ExeterAcademy


PVMT 1 Pleasant Valley HighSchool

SC C SC C SC D SC A

PRISMS Eyas PrincetonInternational Schoolof Math and Science


PRISMS Falcons PrincetonInternational Schoolof Math and Science


Princeton Lion Princeton MathCircle

YC Aud. YC Aud. SC C SC C

Pui Ching PuiChing MiddleSchool Macau




RVMT - A Raritan Valley MathTeam


Raccoon A RIA GlobalEducation


Ridge Lion Ridge Math Circle YC Aud. YC Aud. SC C SC C

RSM RSM SC D Sv 206 SC D SC A

SagerHmmt Sager Education YC Aud. Sv 210 SC C SC C

CS Shanghai AmericanSchool

SC A SC A SC D SC C

SCS Sierra Canyon School YC Aud. Sv 211 SC B SC B

Cardinal South Kent School SC D SC D SC B SC B

SKS Black South Kent School SC D Sv 202 SC B SC B

SMWL St. Mark’s School SC B Sv 204 SC C SC C

SPS-A St. Paul’s School SC E SC E SC D SC C

TAS Taipei Math Circle YC Aud. YC Aud. SC B SC B

Beijing Star TAL SC A SC A SC B SC B

TAMS Texas Academy ofMathematics andScience

SC A Sv 212 SC D SC C

Brearley The Brearley School SC A Sv 213 SC D SC B

Bromfield The BromfieldSchool

SC E SC E SC D SC B

RLS The Roxbury LatinSchool


SBS The Stony BrookSchool

SC 310 SC 310 SC E SC B

TGG The Taft School SC E Sv 215 SC D SC B

WNSX The WillistonNorthampton School

YC Aud. YC Aud. SC C SC C

Saltyfish ThinktownInstitution

SC B10 SC B10 SC E SC B

TT TT Math School YC Aud. Sv 210 SC B SC B

UTS A University ofToronto Schools


UTS B University ofToronto Schools

SC B SC B SC B SC B

Chipmunks Walton High School SC C SC C SC B SC B

Wu-Shu Walton High School SC C SC B SC B SC B

Utah Wasatch Academy SC D Sv 204 SC C SC C



Wasatka Wasatch Academy SC D Sv 205 SC C SC C

Rams Watkinson School YC Aud. Sv 207 SC B SC B

WV West Virginia SC 222 SC 222 SC E SC B

WAMC Westchester AreaMath Circle


WMA Mars Western MassARML


WMA Stars Western MassARML


WMA Suns Western MassARML

SC B SC B SC C SC C

WMA Venus Western MassARML


Western PA WesternPennsylvania


Ghost Math Westford Academy SC A Sv 212 SC B SC B

WestyBlack Westminster School SC C SC C SC C SC C

WestyGold Westminster School SC C SC B SC C SC C

Weston A Weston High School SC 221 SC 221 SC E SC B

Wheeler1 Wheeler School SC D SC D SC B SC B

Wheeler2 Wheeler School SC D Sv 203 SC B SC B

WEHS-A Williamsville EastHigh School


(GMP)’ Williamsville North SC E SC E SC D SC B

WHS 1 Winchester HighSchool

SC A Sv 213 SC B SC B

WAnabees Worcester Academy YC Aud. YC Aud. SC B SC B

Yu’s A Team Yu’s Elite Education SC B Sv 101 SC C SC C

Yu’s B Team Yu’s Elite Education SC B SC B SC C SC C

Yu’s C Team Yu’s Elite Education SC B Sv 102 SC C SC C

Student Schedule

Friday, November 10, 2017 (MIT)

Time Event Location

7:00PM – 8:00PM Early Registration Building E51

7:00PM – 7:45PM Pizza and Ice Cream Building E51

7:45PM – 8:00PM Mini-Events Preview Building E51

8:00PM – 9:00PM Mini-Events Building E51

Saturday, November 11, 2017 (Harvard)

Time Event Location

8:00AM – 9:00AM Breakfast Science Center Lobby

8:00AM – 9:00AM Registration Science Center 112

9:00AM – 10:15AM Individual Round Varies

10:30AM – 11:45AM Theme Round Varies

12:00PM – 1:00PM Team Round Varies

1:00PM – 2:30PM Lunch On Own*

2:30PM – 4:15PM Guts Round Science Center (Varies)

4:20PM – 4:40PM Integration Bee Finals Science Center B

5:00PM – 5:45PM Awards Ceremony Science Center (Varies)

* Teams that pre-ordered pizzas will be able to pick them up in the Science Center Lobbyduring lunchtime.

Coaches, Proctors, and Parents Schedule

Friday, November 10, 2017 (MIT)

Time Event Location

7:00PM – 8:00PM Early Registration Building E51

7:00PM – 7:45PM Pizza and Ice Cream Building E51

7:45PM – 8:00PM Mini-Events Preview Building E51

8:00PM – 9:00PM Mini-Events Building E51

Saturday, November 11, 2017 (Harvard)

Time Event Location

8:00AM – 9:00AM Breakfast Science Center Lobby

8:00AM – 9:00AM Registration Science Center 112

9:15AM – 10:30AM Talk by Po-Shen Loh Jefferson 250

11:15AM – 11:45AM Proctor Meeting Jefferson 250

12:00PM – 1:00PM Team Round Proctoring Varies

1:00PM – 2:30PM Lunch On Own*

2:30PM – 4:15PM Guts Round Viewing Jefferson 250

4:20PM – 4:40PM Integration Bee Finals Science Center B

4:45PM – 5:30PM Awards Ceremony Science Center

A Help Center is located in Science Center 104.

* Teams that pre-ordered pizzas will be able to pick them up in the Science Center Lobbyduring lunchtime.

Test Information

Rules

You may not use books, notes, calculators, pocket organizers, slide-rules, abaci, or anyother computational aids. Similarly, you may not use graph paper, rulers, protractors,compasses, architectural tools, or any other drawing 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 no fractions andis 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 must goto the designated Appeals Room and submit an appeal in writing. The deadline to doso will be announced on the day of the contest.

Decisions of the coordinators of the Harvard-MIT Math Tournament Novem-ber are final.

Local Information

Food

• Clover ($)Vegetarian sandwiches and plates. 1326 Mass Ave.

Cambridge, MA 02138

• Shake Shack ($)American fast casual food, famousburgers and shakes.

92 Winthrop StCambridge, MA 02138

• Felipes ($)Made-to-order fresh Mexican foodwith aunthetic recipes

21 Brattle StCambridge, MA 02138

• Chipotle ($)Mexican fast casual food, includingcustom-made tacos and burritos.

1 Brattle StCambridge, MA 02138

• El Jefes Taqueria ($)Assembled-to-order Mexican eatswith lots of toppings and sauces.

83 Mt Auburn StCambridge, MA 02138

• Subway ($)Build-your-own sandwiches withmany healthy options.

36 John F. Kennedy StCambridge, MA 02138

Emergency

In the event of fire or life-threatening emergency, call (617) 495-1212, not 911. Thisnumber will reach the Harvard Police Department; they will respond faster than 911.

Harvard Campus Map (http://map.harvard.edu/)

http://map.harvard.edu/

HMMT Officers and Staff

Officer Team

Tournament Directors: Andrew He, Nathanael Cho

Problem Czars (November): Ashwin Sah, Michael Tang, Yannick Yao

Problem Czars (February): Allen Liu, Henrik Boecken, Kevin Sun

Finance Directors: Ellen Li, Emily Cheng

Registration Directors: Lillian Zhang, Zachary Diamandis

Schedule Coordinators: Cynthia Liu, Grace Whitney

Scripts Director: Yang Liu

Scripts Team: Alexander Wei, Ashley Kim, Roger Jin

Webmaster: Grace Zhang

Outreach Chairs: Ahaan Rungta, Brice Huang

Social Chair: Celine Liang

General Officer: Emery Liu

Special Projects Directors: Jakob Weisblat, Michelle Chen

Historian: Evan Chen

Staff Members

Assistant Historian: David Liang

Brochure Coordinator: Sarah Wu

Building Coordinators: Andres Fabrega, Cindy Yang, Francisco Proskauer, Jane Ahn,Luke Melas-Kyriazi, Natalia Hajlasz

Driver: William Qian

Finance Associates: Anurag Golla, Isabella Kang, Kim Nguyen, Rebecca Shin

Food Czars: Ting Li, Xiaolu Guo

Guts Round Directors: Daniel Qu, Karen Chen, Sophia Xia

Head Graders: Aaditya Singh, Mark Kong, Nelson Niu

Head Proctor: Matthew Hambacher

Logistics Coordinators: Aditi Chitkara, Sambuddha Chattopadhyay, William Ho

Problem Committee: Alec Sun, Amanda Wang, Angela Deng, Caleb He, CalvinYost-Wolff, Chad Qian, Christopher Shao, Christopher Xu, Cory Hixson, DanielChiu, David Xiang, Dhamanpreet Kaur, Dhruv Rohatgi, Fan Zhou, Faraz Mas-roor, Farrell Wu, Gabriel Mintzer, Jason Lu, John Wu, Johnny Gao, JunyaoPeng, Kevin Chen, Kevin Yang, Mehtaab Sawhney, Mendel Keller, Michael Ku-ral,Nathan Weckwerth, Nikhil Reddy, Qi Qi, Quilee Simeon, Rachel Zhang, SanathDevalapurkar, Saranesh Prembabu, Serina Hu, Sujay Kazi, Varkey Alumootil

Photographers: Abraham Park, Joyce Tian, Steven Hao, Vivian Huang

Prize Czars: Anton Cao, Baula Xu, Byron Xu

Sign Czars: Ben Nguyen, Christina Chen, Kenz Kallal

Spokespersons: Cathy Wang, Hadrian Merced, Justin Yu, Michael Xie, Paolo Adajar,Rogers Epstein, Thomas Xiong, Vaughan McDonald

Sponsors

Special thanks to our sponsors:

21st Harvard-MIT Mathematics TournamentNovember Tournament 2017

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