19 Harvard-MIT Mathematics Tournament - The Harvard

19 Harvard-MIT Mathematics Tournament - The Harvard

19th Harvard-MIT
Mathematics Tournament
HMMT November
Saturday, November 14, 2015
November 14, 2015
Hello HMMT community,
elcome to the 2015 Harvard-MIT November Math Tournament!
After months of writing problems, organizing registration, and developing software, we are thrilled to see all of you in Cambridge. Whether
you’re joining us from Shanghai, Tegucigalpa, or Boston, we hope you’re
as excited as we are!
W
We at HMMT seek to share our passion for mathematical problemsolving. While math itself remains a core piece in our mission, we see
year after year that people are just are as important. Many of us helping to organize HMMT can trace our friendships to events like these, long
after we have graduated. While we won’t speculate why these events engender such lasting bonds, we encourage you to take advantage of this
amazing opportunity. Over breakfast, between rounds, and even during
our ceremonies, introduce yourself to students from other teams. Say hello
to some of our sponsors in Lobby 10. And most importantly, thank your
coaches and parents. As scholars, 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 MIT undergraduates. No matter how many of them you
solve, we hope you find them both challenging and engaging.
To the coaches, teachers, and parent chaperones: thank you for your
dedication to helping your students compete. We have set aside room 4163 as a “coaches’ lounge,” where we will have the proctors’ meeting and
a live stream of the Guts Round scoreboard.
To help navigate the campus, we have included a map inside the program and posted signs to direct you around MIT. Moreover, all teams’
room assignments can be found inside the program. Should you have any
questions, comments, or concerns, please don’t hesitate an HMMT staff
member (dressed in yellow HMMT shirts) for help.
Whether this is your first or fourth HMMT, we hope that you enjoy the
tournament we’ve put together. Good luck today, and above all, have fun!
Regards,
Alex Nie
James Rowan
Tournament Directors
Alex Katz
Sam Korsky
Yang Liu
November Problem Czars
Teams and Room Assignments
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
Team Name
AAE Problem Solving Group
Acton Boxborough
Uber Noobers
Albany Area Math Circle Ordinals
Albany Area Math Circle Cardinals
Albemarle High School
American School of Tegucigalpa Eagles
AMSA Charter 3
AMSA Charter 2
AMSA Charter 1
WIN15
GuangzhouStar
BeijingStar
BH Math Team
BCA 6
BCA 5
BCA 4
Bishop Stang
Brighton High School
BB&N Daze
BB&N Knights
1liuminati
Chelmsford
Chesapeake 2
Chesapeake 1
Terra Belem
Collegiate School
Commonwealth A
Concord Academy 1
Silver
Gold
Coral Falcons
DC Mathletes 1
Deerfield Academy Little Green
Indiv
Team
Guts
Award
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
26-100
26-100
32-123
26-100
4-261
26-100
32-123
26-100
36-112
26-100
32-123
26-100
66-144
26-100
32-123
26-100
56-191
26-100
32-123
26-100
8-205
26-100
32-123
26-100
4-265
26-100
32-123
26-100
56-167
26-100
32-123
26-100
66-160
26-100
32-123
26-100
1-242
26-100
32-123
26-100
56-162
26-100
32-123
26-100
26-328
26-100
32-123
26-100
66-168
26-100
32-123
26-100
56-180
26-100
32-123
26-100
5-217
26-100
32-123
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
Team Name
Deerfield Academy Big Green
Dream Math Beta
Dream Math Alpha
Elite School
Emma Willard School
Gauss Math Circle
Gauss School of Mathematics
Georgetown Day School 1
Gifted Math Program
Groton Zebras 2
Hawks
ICAE2
ICAE1
IDEA (3rd team)
Ideamath Marker
Ideamath Pencil
Chicago All Stars
Individuals 1
Individuals 2
Individuals 3
Individuals 4
Individuals 5
Individuals 6
Individuals 7
Institute of Merit
Jinan
John Bapst Crusaders
Jonas Clarke (MS)
Las Vegas Math Circle A++
Las Vegas Math Circle A+
Lexington Epsilon
Lexington Delta
LexMath C
LexMath B
LexingtonRock
Indiv
Team
Guts
Award
26-100
4-265
26-100
32-123
26-100
4-257
26-100
32-123
26-100
4-153
26-100
32-123
26-100
36-155
26-100
32-123
26-100
66-144
26-100
32-123
26-100
36-153
26-100
32-123
26-100
36-112
26-100
32-123
26-100
4-159
26-100
32-123
26-100
66-144
26-100
32-123
26-100
4-257
26-100
32-123
10-250
10-250
26-100
34-101
10-250
10-250
26-100
34-101
10-250
10-250
26-100
34-101
10-250
10-250
26-100
34-101
10-250
10-250
26-100
34-101
10-250
10-250
26-100
34-101
10-250
10-250
26-100
34-101
10-250
10-250
26-100
34-101
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
10-250
26-100
10-250
10-250
4-159
26-100
10-250
10-250
4-153
26-100
10-250
10-250
56-167
10-250
10-250
10-250
26-328
10-250
10-250
10-250
36-156
10-250
10-250
10-250
66-154
10-250
10-250
10-250
5-234
10-250
10-250
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
Team Name
Crownless Kings
PEA Livingston
Livingston STFX
Londonderry HS 1
Loomis Chaffee Grey
Louisiana Math Circle Team B
Louisiana Math Circle Team A
Medford Mathletes
Millburn High School
Milton Academy
Montana Math Team
Morgantown High 1
Mystic Valley Regional Charter
School 1
Hacking Hit
Newton North Cubs
Newton North Tigers
Newton South Tangents
Newton South Cosines
Newton South Sines
NMH Hogger 2
NMH Hogger 1
Rice Krispies
Northview A
Phi
Phillips Academy A2
Phillips Academy A1
PEA IDEA MATH United
PEA Lad(ie)s in Lavender
PEA Children in Chartreuse
PEA Kids in Khaki
PEA Red
Pinnacle 1
Raritan Valley Math Team
Ridge Math Circle
ABRHS
Indiv
Team
Guts
Award
10-250
4-145
10-250
10-250
10-250
36-112
10-250
10-250
10-250
4-261
10-250
10-250
10-250
36-144
10-250
10-250
10-250
26-142
10-250
10-250
10-250
4-159
10-250
10-250
10-250
36-153
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
34-101
10-250
10-250
34-101
36-155
10-250
10-250
34-101
8-205
10-250
10-250
34-101
66-160
10-250
10-250
34-101
26-142
10-250
10-250
34-101
66-160
10-250
10-250
34-101
4-261
10-250
10-250
34-101
5-217
10-250
10-250
34-101
36-155
10-250
10-250
34-101
56-169
10-250
10-250
34-101
66-168
10-250
10-250
34-101
38-166
10-250
10-250
34-101
36-156
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
Team Name
RPS2
RPS1
SFLS1
SFLS2
Sharon Alpha
Somerville High School 1
SSA1
St. Mark’s School
SPS 2
SPS 1
Red Rhinos
Roxbury Latin 3
Roxbury Latin
Sexy Bears
Grasping of the ghostdom
Chicago Madness
University High School
UTS B
UTS A
Walton C
Walton B
Walton A
TianjinStar
Beijing Wanmu Team 1
Wasatch Academy DNE
Wasatch Academy WAbsolutes
Westchester Area Math Circle
Western Mass ARML Moons
Western Mass ARML Suns
Western Mass ARML Stars
Western Mass ARML Pluto
Western PA ARML
Westford Academy
Westminster Gold
Westminster Black
Indiv
Team
Guts
Award
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
32-123
10-250
10-250
32-123
36-156
34-101
34-101
32-123
66-168
34-101
34-101
32-123
26-168
34-101
34-101
32-123
5-234
34-101
34-101
32-123
26-310
34-101
34-101
32-123
66-154
34-101
34-101
32-123
66-144
34-101
34-101
32-123
56-162
34-101
34-101
32-123
36-144
34-101
34-101
32-123
4-145
34-101
34-101
32-123
66-154
34-101
34-101
66-168
26-322
34-101
34-101
66-144
56-169
34-101
34-101
5-217
1-242
34-101
34-101
66-168
4-153
34-101
34-101
66-144
66-160
34-101
34-101
66-168
56-180
34-101
34-101
66-144
4-265
34-101
34-101
66-144
26-168
34-101
34-101
66-168
66-154
34-101
34-101
66-144
56-191
34-101
34-101
4-153
26-322
34-101
34-101
4-159
56-180
34-101
34-101
4-153
36-112
34-101
34-101
4-153
26-302
34-101
34-101
4-153
4-153
34-101
34-101
4-159
4-145
34-101
34-101
140
141
142
143
144
145
146
147
148
Team Name
Weston Alpha
White Ridge
William Fremd High School
Winchester 2
Winchester 1
Worcester Academy Team 2
Worcester Academy Team 1
Yu’s Buffalo
Yu’s Alligator
Indiv
Team
Guts
Award
4-159
1-134
34-101
34-101
5-234
66-168
34-101
34-101
5-234
26-310
34-101
34-101
5-234
5-217
34-101
34-101
5-217
1-134
34-101
34-101
5-234
26-302
34-101
34-101
5-217
38-166
34-101
34-101
66-168
36-153
34-101
34-101
5-217
5-234
34-101
34-101
Schedule of Events
Friday, November 13, 2015 (Harvard)
Time
Event
Location
7:00PM – 8:00PM
Early registration
Maxwell-Dworkin
7:00PM – 7:45PM
Pizza dinner
Maxwell-Dworkin
7:45PM – 8:00PM
Ice cream
Maxwell-Dworkin
8:00PM – 9:00PM
Mini-events
Maxwell-Dworkin
Saturday, November 14, 2015 (MIT)
Time
Event
Location
8:00AM – 9:00AM
Breakfast
Lobby 13
8:00AM – 9:00AM
Registration
Lobby 10
8:30AM
Indv Competitor Meeting
4-163
9:00AM – 10:00AM
Individual Round 1
Varies
10:00AM – 11:00AM
Individual Round 2
Varies
10:45AM
Proctor Meeting
4-163
11:30AM – 12:30PM
Team Round
Varies
12:30PM – 2:00PM
Lunch
Pizza outside 10-250
2:15PM – 3:45PM
Guts Round
26-100, 10-250, 34-101
4:00PM – 5:00PM
Awards
10-250, 32-123, 34-101
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. 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 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 for a morning
event is incorrect, an appeal must be submitted at Lobby 10 by 1:30 pm.
If the protest concerns an afternoon event, the appeal must be submitted
as soon as possible after the Guts Round.
Decisions of the coordinators of the Harvard-MIT Math Tournament November are final.
Local Information
Lodging
• Le Meridien Cambridge-MIT
20 Sidney Street, Cambridge, MA 02139
(617)-577-0200
• The Kendall Hotel
350 Main St, Cambridge, MA 02142
(617)-577-1300
• Boston Marriott Cambridge
50 Broadway, Cambridge, MA 02142
(617)-494-6600
Food
Student Center (W20)
Kendall Square
• Anna’s Taqueria
Student Center (W20) first floor
• Au Bon Pain
238 Main Street
• Dunkin Donuts & Cambridge Grill
Student Center (W20) first floor
• Chipotle Grill
2 Cambridge Center
• Lobdell Food Court
Student Center (W20) second floor
• Clover (Vegetarian)
5 Cambridge Center
–
–
–
–
Café Spice
Shawarma Shack
Shinkansen Japan Fast Food
Subway
• Cosi
290 Main Street
• Rebecca’s Cafe
290 Main Street #4
Emergency
In the event of fire or life-threatening emergency, call (617) 253-1212 instead
of 911.
MIT Campus Map
(http://whereis.mit.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, Sandeep
Silwal, Justina Yang
Finance Associate: Francisco Rivera
Food Czars: Ying Gao, Xin Wen
Guts Round Directors: Andrew He, Rick Huang, Andrew Jiang, Varun Mohan
Head Graders: Jessie Chi, Kevin Liu
Head Proctor: Lily Zhou
Hosting Coordinators: Nathanael Cho, Jeewoo Kang
Photographers: Korrawat Pruegsanusak, Linda Zhang
Prize Czars: Nicholas Wu, 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
Programme prepared by Ahaan Rungta and William Qian, and typeset by Evan Chen.
Sponsors
Special thanks to our sponsors:
19th Harvard-MIT Mathematics Tournament
November Tournament 2015