19th harvard-mit mathematics tournament · pdf filew elcome to the 2016 harvard-mit february...

19th Harvard-MITMathematics Tournament

HMMT February

Saturday, February 20, 2016

February 20, 2016

W elcome to the 2016 Harvard-MIT February Math Tournament. Weat HMMT are dedicated to promoting mathematical problem solv-

ing to high school students. We are thrilled to see all of you in Cambridge,and we hope you’re as excited as we are.

Throughout our history, we have aimed to foster passion for and enjoy-ment of mathematics. While the math itself is a big part of that, we feelthat the people are just as important. You’re here with nearly 800 of thebrightest, most mathematically-gifted students in the world! So to takeadvantage of this unique opportunity introduce yourself to students fromother teams. Many of us on the HMMT organizing team can trace ourfriendships back to moments like these. As usual, all of our problems arewritten and compiled by Harvard and MIT undergraduates, many formerHMMT competitors themselves. No matter how many of them you solve,we hope you find the problems challenging and engaging. Above all else,we hope that you have fun!

Should you have any questions, comments, or concerns at any pointduring the tournament, please feel free to ask an HMMT staff member forhelp (we are all in green). If you don’t know where you should be, pleaserefer to the schedule and map found in this program or, when in doubt,find a staff member.

Whether this if your first year at HMMT or you’ve competed before,good luck today and enjoy your time at HMMT February 2016.

Sincerely,

Alex NieJames RowanTournament Directors

Evan ChenSammy LuoFebruary Problem Czars

Teams and Room Assignments

Teams are listed alphabetically by team name (not organization name).

• E105, E210 = Emerson 105, Emerson 210

• J250 = Jefferson 250

• Yen. = Yenching Auditorium

• Rob. = Robinson

• Emer. = Emerson

• A, B, C, D, E = Science Center lecture halls A, B, C, D, E

ID Team Name Individual Team Guts Awards

1 AAE Problem SolvingGroup A Team

Yen. Rob. 107 D D

3 Amador Valley/PleasantonHigh School

E105 Rob. 105 C C

7 Beijing China STFX Edu-cation INC 1

E105 E105 C C

8 BeijingMath D C J250 B

11 Chicago Twilight Sparkle D D J250 B

12 Choate Yen. Sever 201 D D

13 Chuninators C C C C

15 East Brunswick HS J250 Sever 307 Yen. B

16 Eureka D Sever 106 J250 B

17 Florida A C Sever 206 C C

19 FMC C’est La Vie J250 Sever 210 J250 B

20 Groton Zebras E105 E105 C C

21 Henry M. Gunn HighSchool

Yen. Rob. 107 D D

22 HFI C Sever 113 C C

23 Hockaday E210 Sever 210 J250 B

24 Hotchkiss Blue A Sever 109 Yen. C

25 HS Affiliated to PekingUniversity

E105 E105 C C

26 IDEAMATH PEA United E210 Sever 303 J250 B

27 Illinois Mathematics andScience Academy

J250 Sever 306 Yen. B

28 Kent Lions J250 Sever 110 Yen. B

29 KGSEA KOREA A C A Yen. B


30 KGSEA Korea B C C Yen. B

31 Knights A E210 E J250 B

32 Knights B E210 C J250 B

33 Lawrenceville Yen. Yen. J250 B

34 Lehigh Valley Fire A Sever 102 Yen. B

35 Lehigh Valley Ice A Sever 103 Yen. B

36 Lehigh Valley Lightening A Sever 104 Yen. B

37 Lehigh Valley Thunder J250 Sever 113 Yen. B

38 Lexington Alpha Yen. Sever 212 D D

39 Lexington Beta Yen. Sever 307 D D

40 Loomis Chaffee Pelicans E105 E105 C C

41 MG Varna C Sever 102 Yen. B

42 Minnesota Gold 1 A A C B

43 Minnesota Gold 2 A E Yen. B

44 Misery A Sever 208 D D

45 Montgomery Blair 1 Yen. Sever 205 D D

46 Montgomery Blair 2 Yen. Sever 308 D D

47 Nanjing Foreign LanguageSchoo

D Sever 208 D D

48 NCSSM E105 Sever 113 C C

49 NFLS E105 Sever 207 C C

50 Northeastern E105 Sever 113 C C

51 NYC Team 1 D Sever 306 D D



54 Object C Sever 107 C C

55 OCMC Yen. Yen. D D

56 Octachorons E105 Sever 110 C C

57 PEARL E210 Sever 211 J250 B

58 Perfetch E105 Emer. 210 C C

59 Perfetch2 E105 E105 C C

60 Phillips Academy 1778 Yen. Rob. 105 Yen. B

61 Phillips Academy 2016 Yen. Rob. 106 Yen. B

62 Pirates A E105 Sever 215 C C

63 Pirates B E105 Sever 302 C C

64 PMG Bourgas E210 Sever 107 Yen. B

65 Princeton InternationalSchool of Math and ScienceA

C Sever 110 C C


66 Princeton InternationalSchool of Math and ScienceB

C Sever 306 C C

67 rdfz Icc E105 Emer. 210 C C

68 Renmin 2 D Sever 207 D D

69 Roxbury Latin 2 Yen. Yen. D D

70 sfls razorback E105 Sever 103 C C

71 Shenzhong Nirvana D Sever 113 D D

72 Shenzhong Phoenix D Sever 112 D D

73 SMG Sofia C Sever 209 Yen. B

74 St. Mark’s School of Texas C Sever 103 C C

75 Star League A-Star Air C A Yen. B

76 Star League A-Star Earth C D Yen. B

77 Star League A-Star Fire C C Yen. B

78 Stir Leg B+ Dirt J250 J250 Yen. B

79 Team Paly E210 E J250 B

80 Tennessee J250 J250 Yen. B

81 Texas Horned Toads A A Yen. B

82 Texas Lobos A C Yen. B

83 The Harker School D Sever 204 D D

84 The HS affiliated to Ren-min Univ

D Sever 206 D D

85 Thomas Jefferson A J250 Sever 210 J250 B

86 Thomas Jefferson B J250 Sever 303 J250 B

87 Thomas Jefferson C J250 Sever 305 J250 B

88 Troy1 E105 Emer. 210 D D

89 Washington Gold E105 Sever 113 C C

90 Western Mass ARML Stars D Sever 109 J250 B

91 Westford Academy A C Sever 106 C C

92 York Stars Yen. Rob. 205 D D

93 Individuals 1 C C C B

94 Individuals 2 C C C B

95 Individuals 3 D D D B

96 Individuals 4 E210 E210 J250 B

Schedule of Events

Friday, February 19, 2016 (MIT)

Time Event Location

7:00PM – 8:00PM Early registration Walker Memorial

7:00PM – 7:45PM Pizza and ice cream Walker Memorial

7:45PM – 8:00PM Mini-events descriptions Walker Memorial

8:00PM – 9:00PM Mini-events Buildings 2 and 4

Saturday, February 20, 2016 (Harvard)

Time Event Location

8:00AM – 9:00AM Breakfast NW Building

8:00AM – 9:00AM Registration NW Building

8:30AM Indv Competitor Meeting NW Building

9:00AM – 10:00AM Algebra Round Varies

10:00AM – 11:00AM Geometry Round Varies

11:00AM – 12:00PM Combinatorics Round Varies

11:15AM Proctor Meeting Jefferson 356

12:15PM – 1:15PM Team Round Varies

1:30PM – 2:30PM Lunch *

2:30PM – 4:00PM Guts Round Varies

4:00PM – 4:30PM Guest performances Science Center

4:30PM – 5:00PM Awards Science Center

* If your organization pre-ordered pizza, it will be available in the building your

teams are taking the team round. Otherwise, teams are on their own for lunch.

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 for a morningevent is incorrect, an appeal must be submitted outside Science Center C dur-ing lunchtime. If the protest concerns an afternoon event, the appeal must besubmitted as soon as possible after the Guts Round.

Decisions of the coordinators of the Harvard-MIT Math TournamentFebruary are final.

Local Food

• Tasty Burger

40 John F. Kennedy StCambridge, MA 02138

Relaxed venue serving a variety of burgers until 4AM ($)

• Shake Shack

92 Winthrop StCambridge, MA 02138

Well-known chain serving a variety of foods, including burgers and shakes($)

• Felipe’s

21 Brattle StCambridge, MA 02138

Made-to-order fresh Mexican food with authentic recipes ($)

• Chipotle

1 Brattle SquareCambridge, MA 02138

Mexican food chain offering custom made burritos, bowls, and tacos ($)

• El Jefe’s

83 Mt Auburn StCambridge, MA 02138

Assembled-to-order tacos, burritos, and other Mexican eats with a varietyof sauces and toppings ($)

• Subway


Build-your-own sandwich chain with many healthy offerings ($)

• Chutney’s


Modern eatery serving Indian style food in the form of a wrap, rice bowl orpanino ($)

• Panera

1288 Massachusetts AveCambridge, MA 02138

Bakery/cafe chain serving sandwiches, salads, soups and more ($)

• Al’s


Take-out cafe known for their sandwich, soda, and chips bag lunch ($)

• Qdoba


Mexican chain for custom burritos, tacos, and more ($)

• Clover

7 Holyoke StCambridge, MA 02138

Health conscious cafe featuring an ever-changing menu with foods createdwith fresh, local ingredients ($)

• Au Bon Pain


Chain cafe serving sandwiches, soups, and salads along with breads andother baked goods ($$)

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

http://www.map.harvard.edu/

HMMT Officers and Staff

Officer Team

Tournament Directors: Alex Nie, James Rowan

November Problem Czars: Alex Katz, Sam Korsky, Yang Liu

February Problem Czars: Evan Chen, Sammy Luo

Registration Director: David Liang

Finance Director: Haoqing Wang

Scripts Team: Jakob Weisblat, Jason Liang, Marcus Boorstin

Webmaster: Vahid Fazel-Rezai

Social Chairs: Jessica Wang, Jon Lu

Data Czar: William Qian

Outreach Chairs: Akshay Ravikumar, David Mende

Staff Members

Building Coordinators: Angela Cai, David Gold, Sruthi Narayanan, SandeepSilwal, Justina Yang

Finance Associates: Francisco Rivera, Vivek Miglani

Food Czars: Ying Gao, Xin Wen

Guts Round Directors: Andrew He, Rick Huang, Andrew Jiang, Varun Mo-han

Head Graders: Jessie Chi, Kevin Liu

Head Proctor: Lily Zhou

Hosting Coordinators: Nathanael Cho, Jeewoo Kang

Photographers: Korrawat Pruegsanusak, Linda Zhang

Prize Czars: Lisa Yang, Miguel Young

Problem Committee: Brice Huang, Pakawut Jiradilok, Kritkorn Karntikoon,Joseph Kuan, Juan Ortiz Rhoton, Ahaan Rungta, Ashwath Thirumalai,Danielle Wang, Jianqiao Xia, Kevin Yang, Yunkun Zhou, Tony Zhang

Sign Czar: Mary Zhong

Spokespersons: Rogers Epstein, Yufeng Ling, George Zhang, Nicholas Wu

And many day-of volunteers

High school seniors: interested in helping run HMMT next year? Email us at hmmt-request@

mit. edu .

Programme prepared by the HMMT staff and typeset by Evan Chen.

[email protected]

[email protected]

19th Harvard-MIT Mathematics TournamentFebruary Tournament 2016

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19th harvard-mit mathematics tournament · pdf filew elcome to the 2016 harvard-mit february...

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