The MBTA Map, and Unexpected Detail

If you live in the Boston area, I have a geographical mind-jogger for you.

Considering only light and heavy rail stations (so, including the five colored lines, but excluding buses and the commuter rail):

1) Which station is the closest to the geographical midpoint between Alewife and Braintree?
2) Which station is the closest to the geographical midpoint between Forest Hills and Oak Grove?
3) Which station is the closest to the geographical midpoint between Lechmere and Riverside?
4) Which station is the closest to the geographical midpoint between Bowdoin and Wonderland?
5) Which station is the closest to the geographical midpoint between Chelsea and Dudley?

And you could look at the map above, because it won’t help you much.

If you’re familiar with several metro/subway maps, you probably know by now that they aren’t drawn to scale. The MBTA, however, has a feature that several other system maps also have that might make one think the map is remotely to scale: it depicts bodies of water in the system area.

And not only does it bother to depict the water, it bothers to depict it with substantial accuracy: the shape of the waterways on the map really do resemble the actual geographic shapes of the coastline and the rivers to a surprising level of detail. It even bothers to clarify the lagoon at Castle Island.

On the other hand, the actual rail lines are nowhere near that straight.

So here’s a question: does the accuracy of water details give the map reader a false impression of geographic accuracy in the rail lines depicted?

In any case, it’s quite impressive that one map manages to juxtapose such a careful attention to accuracy in bodies of water with such a bare-bones depiction of the system lines, a discrepancy in detail that feels like a challenge to achieve.

To what degree of discrepancy? Well, here’s the answers.

1) Fields Corner is closest to halfway between Alewife and Braintree.
2) Kendall is closest to halfway between Forest Hills and Oak Grove.
3) Boston College is closest to halfway between Lechmere and Riverside.
4) Wood Island is closest to halfway between Bowdoin and Wonderland.
5) Haymarket is closest to halfway between Chelsea and Dudley.

Advertisements

A Geographical Puzzle Based on the Electoral College

Find a set of states of the US such that:

  • No pair of them border each other.
  • Their electoral votes combine to at least 270, the quantity needed to win a presidential election.

This is actually very difficult. I’d be extremely impressed if anyone can do this without looking at an electoral college map.

This puzzle somewhat demonstrates the unusually decentralized and relatively evenly distributed nature of the US’s population, as well as the dampening effect of voting power imbalance prescribed by the electoral college.

Another Only Connect Game

I wrote another Only Connect that I presented on Floor Pi. This one was really close, where the two teams had scores of 23 and 22, decided by the last item.

MIT context is not necessary for any items in the first two rounds.

Round 1: Connections
Canada | Yosemite | United Arab Emirates | aboriginal
Answer: Consonants and Vowels Alternate
[was an audio question]
Mahler’s Fifth Symphony | Rachmaninoff’s Op. 3 No. 2 Prelude | Chopin’s Fantasie-Impromptu | Beethoven’s Moonlight Sonata
Answer: Classical Music in C-Sharp Minor
Frederick Sanger | Marie Curie | Linus Pauling | Office of the United Nations High Commissioner for Refugees
Answer: Multiple-Time Recipients of the Nobel Prize
Saxony | Denmark | Brandenburg | France
Answer: Switched Sides in the Thirty-Years War
fur | abjurer | vex | tang
Answer: English Words that rot13 to Other English Words

Round 2: Sequences
Suffolk | New York | Queens | Kings
Answer: Highest-Population Counties in New York
635318657 | 1729 | 50 | 4
Answer: Smallest Number that can be Written as the Sum of Two nth Powers of Positive Integers Two Distinct Ways
te | mind | birdplane | star
Answer: Last Words of Last Versus of the Four Chord Song
Zulu | Sesotho | Afrikaans | English
Answer: Languages of Consecutive Sections of South Africa’s National Anthem
Poseidon | Ouranos | Cronus | Zeus
Answer: Planets by Greek Equivalents of Roman Gods
Tunisia | Egypt | Libya | Yemen
Answer: Countries whose Governments were Overthrown in the Arab Spring, in Chronological Order

Round 3: Connecting Wall
Third
Fourth
North
Red
Black
Ha-ha
Bryce
Street
Fifth
Copley
Fulkerson
Kings
Maverick
Sciarappa
Grand
Dewey
Answers:
Wall
Canyon National Parks of the USA
Squares in Boston
North-South Streets in East Cambridge

Angola
Angora
Female
Elmo
Horatio
Icosium
Edgar
Loohooloo
Oea
Edo
Mercury
Benvolio
Guenette
Lucius
Read That
Spike Lesson

Answers:
Characters in Shakesperean Plays that Survived to the End Despite Many Characters Dying
Country Capitals, Back in the Day
Art Installations on MIT’s Campus
Avengers (Female: Iron Man, Mercury: Quicksilver, Read That: Scarlet Witch, Spike Lesson: Thor)

Round 4: Missing Vowels
Unfortunately Named Concepts in Mathematics
KLLNGFLD
CXRNG
TTSGRP
HMCDLCHFRPRBLM
Answers: Killing Field, Cox Ring, Tits Group, Homicidal Chauffeur Problem
Musical Modes
LDN
NN
LN
RBN
Answers: Lydian, Ionian, Aeolian, Arabian
Meta
PZZLHNT
DCHLRBNZN
VNTHSCRNM
NLCNNCT
Answers: Puzzle Hunt, 1,3-dichlorobenzene, Even this acronym, Only Connect
Georgia
TLNT
STHSST
THSTH
SNDWCHSLNDS
Answers: Atlanta, South Ossetia, The South, Sandwich Islands
Categories in Floor Pi Only Connects
MMRBLLRCS
PHSSFMTSS
CTGRSNFLRPNLCNNCTS
SPLRS
Answers: Memorable Lyrics, Phases of Mitosis, Categories in Floor Pi Only Connects, Spoilers
Induction
BSCS
STMCLLS
HLLFFM
DCKTB
Answers: Base Case, Stem Cells, Hall of Fame, Duck Tibia
Spoilers
JHNDSTTHND
THMSWNTHMWR
THLSTCTGRSSTTS
MCRRGNSMS
Answers: John Dies at the End, The Emus Win the Emu War, The Last Category is “States”, Microorganisms
States
DNL
PRCLMS
BSNSTNCNDNST
GRG
Answers: Denial, Proclaims, Bose-Einstein Condensate, Georgia

An Only Connect Game

I wrote a game of Only Connect which I hosted for Floor Pi this past night. Here’s the items in the Only Connect game. If you’re not familiar with Only Connect, you could read up how the four rounds work here.

Several of these hints depend on an MIT context.

Clues beyond the first clue (for the first two rounds) and answers are in white text. Highlight to see.

Yeah, I know, this presentation leaks some meta-information beforehand. Deal with it.

Round 1: Connections
decay | less | gloss | wuss
Answer: Words that Become Cities when Said before ‘ter’
50 | 19 | 26 | 82
Answer: Atomic Numbers of Elements whose Symbols are Unrelated to their English Names
50 | 12 | 27 | 5
Answer: Numbers of Stars on Some Country’s Flag
50 | 64 | 51 | 32
Answer: MIT Buildings Not Usually Referred to by their Building Numbers
51 | 1001 | 501 | 11
Answer: Numbers whose Roman Numerals are also Valid Chinese Names
we | seem | sea | yeah
Answer: English Words that Sound like ‘Yes’ in Other European Languages

Round 2: Sequences
x | r | q | j
Answer: English Consonants that Don’t Typically Make the Sounds Represented by Them in IPA
f3 | e5 | g4 | Qh4#
Answer: Fool’s Mate
Rhode Island | Alaska | New York | Hawaii
Answer: US States with Highest Proportions of Population Living on Islands
θ | ζ | ε | β
Answer: Greek Letters that Contain Other Greek Letters in their English Names
123 | 101 | 250 | 100
Answer: Room Numbers of Largest Lecture Halls at MIT
50 | 2 | 2 | 1
Answer: Panels of Loss Meme Interpreted as Roman Numerals

Round 3: Connecting Wall
Triple Alliance
Ranch
Spanish Succession
Roses
Star Market
Kanye
Cosi
Evanston
Yellowknife
Woolsey
Ferguson
Monsoon
River
Passage
Harvest
Pacific
Answers:
War of the ______
2018 Major California Wildfires
Recently Closed Stores in Cambridge, MA
Northwest

Missouri
Connecticut
Surya
Prospect
Mountain
Arkansas
Eastern
Massachusetts
Ohio
Pavilion
Western
Central
River
Passage
Harvest
Pacific
Answers:
Major US Rivers
Indian Restaurants in Cambridge, MA
Streets that Intersect in Central Square
US Time Zones

Round 4: Missing Vowels
Amino Acids
PHNLLNN
SPRGN
TRPTPHN
PRRLSN
Answers: Phenylalanine, Asparagine, Tryptophan, Pyrrolysine
[redacted category]
Numbers that have Appeared So Far in this OnlyConnect
LVN
SXTFR
GHTTW
NHNDRDNDTWNTTHR
Answers: Eleven, Sixty-Four, Eighty-Two, One Hundred and Twenty-Three
MIT Student Groups
LCTRSRSCMMTT
THTCH
HMS
SSCTNFSTDNTCTVTS
Answers: Lecture Series Committee, The Tech, Ohms, Association of Student Activities
Canals
SZ
PNM
R
RT
Answers: Suez, Panama, Erie, Root
Roman Numerals of Prime Numbers
L
XXXV
CXXV
CXCX
Answers: LIII, XXXVII, CXXVII, CXCIX

Best Chess Puzzles

This is a selection of 16 chess puzzles that I find to be among the most incredible and ingenious that I’ve seen.

I have modified the presentation of several of these problems. Most notably, the checkmate problems are usually presented as a “Mate in n”, where n is given to the solver. In these cases, I leave it up to the solver to try to force a mate as quickly as possible. If you want the values of n for these problems, they are listed under the section “The Numbers”, after “The Puzzles” and before “The Solutions”.

The Puzzles

A.

loyd_1

White to play. How quickly can White force a mate?

B.

taverner

White to play. How quickly can White force a mate?

C.

langstaff

White to play. How quickly can White force a mate?

D.

giegold3

White to play. How quickly can White force a mate?

Continue reading “Best Chess Puzzles”

Guess the Statistic

Guess what each of these statistics is, given the top 8 countries.

Statistic 1
1. Denmark
2. Canada
3. Russia
4. Norway
5. United States
6. Finland
7. Sweden
8. Iceland

Statistic 2
1. Australia
2. China
3. Thailand
4. India
5. Israel
6. Mexico
7. United States
8. Philippines

Statistic 3
1. United States
2. El Salvador
3. Turkmenistan
4. Maldives
5. Cuba
6. Thailand
7. Bahamas
8. Seychelles

Statistic 4
1. India
2. Palau
3. Côte d’Ivoire
4. Pakistan
5. United States
6. Australia
7. Nigeria
8. Tanzania
(though there exist good arguments some positional switches should happen)

Statistic 5
1. Bolivia*
2. Ecuador*
3. Colombia
4. Ethiopia
5. Bhutan
6. Eritrea
7. Yemen
8. Mexico
*though there exists a good argument that Ecuador and Bolivia switch places

Statistic 6
1. Russia
2. Kyrgyzstan
3. Canada
4. United States
5. Indonesia
6. Norway
7. Tajikistan
8. Argentina

Statistic 7
1. Venezuela
2. San Marino
3. Costa Rica
4. Panama
5. Ecuador
6. Uruguay
7. Colombia
8. Iceland

Statistic 8
1. India
2. Pakistan
3. China
4. United Kingdom
5. Bangladesh
6. Indonesia
7. Brazil
8. United States