Solution to Connections

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Answer: WIRE

by Anderson Wang

After solving some of the clues, we can notice that there are many pairs of words which only differ by one letter, and there are also many words that combine to make two-word phrases. It turns out that the pieces within each group can be connected such that all horizontal connections make two-word phrases or compound words, and all vertical connections differ by exactly one letter (just like a word ladder). For example, in the first section, {Certain Starbucks size}=TALL connects to {Status or reputation}=STANDING on its west edge, {Instruction}=ORDER on its east edge, and {____ effect (physical phenomenon involving magnetism)}=HALL on its south edge.

Additionally, each group of clues is missing exactly one piece, and the word on this piece can always be uniquely deduced from the adjacent words (and in all cases, there are exactly 2 adjacent words). For example, when we put together all the pieces in the first group, there is nothing that connects on the east side of {Certain precipitation}=RAIN, as well as the west side of {Friend in Australia}=MATE. We can fill in this space with CHECK, which makes two-word phrases with RAIN on the west side and MATE on the east.

Here are the answers to all the clues and how they connect, with the missing pieces highlighted in red:

Gratis FREE
Status or reputation STANDING
Certain Starbucks size TALL
Instruction ORDER
1040, e.g. FORM
___ effect (physical phenomenon involving magnetism) HALL
Certain precipitation HAIL
Common wetland bird RAIL
Something often not included BATTERY
Piece of DNA? ACID
Certain precipitation RAIN
CHECK
Friend in Australia MATE
Knight's aide SQUIRE
Mire BOG
1849 or 1936 SQUARE
Word before and after "or no" DEAL
Food often responsible for gas BEAN
Purse or satchel BAG
Out of charge DEAD
Completely exhausted BEAT
Tourist attraction SIGHT
Status of some e-mails READ
HEAT
Stadium movement WAVE
Black ball EIGHT
Exciting soccer event SAVE
One can be warm or cold FRONT
Veranda PORCH
Lifting equipment JACK
Winter morning sight FROST
Want LACK
Musical riff LICK
2009 animated film with talking dogs UP
Quantity measured in BPM TEMPO
LINK
Relative of a stoat MINK
Layer of paint COAT
By far the best in a category, briefly GOAT
"Say ____!" CHEESE
What it's like outside, per a popular song COLD
Vocation CALLING
21 proof? CARD
HOLD
D&D class BARD
Angelic HOLY
Most of the human body, it's said WATER
It's rude to flip it BIRD
Amorous start? POLY
Piece of a Kit Kat WAFER
Like the air on Mount Everest THIN
Applejack, e.g. PONY
Mary-Kate, for one TWIN
Average MEAN
Spooky sound MOAN
Reap HARVEST
Drop behind? MOON
Word on some traffic signs WALK
Something very relatable, in modern slang MOOD
Start to morning or night GOOD
A knight might try to accomplish one, in a puzzle TOUR
GOLD
Zerg activity RUSH
Word often abbreviated as its sole silent letter HOUR
Annual season FLU
Absolutely nail, in slang SLAY
Wing it? FLY
Meh BLAND
It's fired by some artists CLAY
Make less healthy, in a way FRY
Hormone producer GLAND
Family group CLAN
Tear up CRY
Pamper BABY
Ten Benjamins GRAND
Become an expert in MASTER
PLAN
Superlative BEST
Action on Facebook or Discord FRIEND
It might be shaken off RUST
Asteroid composition BELT
Stratagem RUSE
Stood up ROSE
Eden, e.g. GARDEN
Hodgepodge VARIETY
Take the L LOSE
Zero, in some games LOVE
SEAT
Core essence MEAT
Half a ___ is better than none LOAF
HEAD
Object whose color was much debated in 2015 DRESS
Polo, e.g. SHIRT
Aid in some prayer BEAD
Sam's home, in fiction SHIRE
Mama or Papa, in a fairytale BEAR
Advertise MARKET
Stock unit SHARE
It often leaves a bitter taste BEER
Source of some pressure PEER
Outdoor bowling locale LAWN
PARTY
It might be curried FAVOR
Occasion to rise to? DAWN
Truly enjoy SAVOR
Willing, colloquially DOWN
It's kept by a conductor TIME
Frugal person, often SAVER
Cap's counterpart GOWN
All alternative TIDE
Combine POOL
Hired mercenary GOON
Surveying instrument? POLL
TYPING LIKE THIS, MAYBE SHOUTING
Material applied to bows ROSIN
Court action SHOOTING
STAR
Like many prize money amounts ROUND
Half of the Dynamic Duo ROBIN
Attempt STAB
With "up", like a speaking doll WOUND
Something you might want to buy, but not get TICKET
Tiny pencil STUB
Counterpart of complete, in logic SOUND
Morsel BITE
Sporting object shaped like the Monster logo WICKET
Either of two humors BILE
Send MAIL
BOX
Make multiple small incisions SCORE
Typical hangout for teenagers MALL
Squirrel away STORE
When you might say, "Winter is coming" FALL
Bet against, in a sense SHORT
Floor STORY
Crossword contents, colloquially FILL
Where many castles are built SHORE
Sentry PATROL
Subject of cinema FILM
One might be "of the arts" PATRON
Break into pieces SHATTER
Transpose SWAP
Separate, like a group of rats SCATTER
Spreadsheet feature PLOT
Where definitely not to go when social distancing BAR
Melodramatic show SOAP
Place for a quarter SLOT
It might be jacked CAR
Like many things on Black Friday CHEAP
SHOT
Spam container CAN
Denzel Curry, for Billie Eilish's 2019 tour OPENER
Cut corners CHEAT
One expressing thoughts OPINER
Red or white, perhaps WINE
Slowly decline WANE
Desire WANT
Persevere LAST
Building material in a fairytale STRAW
Delay WAIT
LIST
Purse part STRAP
Pants suspender? HANGER
What's at the end of the line? BAIT
What a sign in front of deep water might say DANGER
Eighth Amendment concern BAIL
Symbol for conjugate transpose in quantum mechanics DAGGER
Reed's place MARSH
Kind of criminal group TRIAD
What some bands do MARCH
Certain lagomorph HARE
Common fairytale villain WITCH
Event with objection-able language? TRIAL
Detest HATE
Hands on a wrist? WATCH
PLAY
What a person awoken from a coma may ask for DATE
Tinder success MATCH
Use one finger, perhaps POINT
"Eat, ____, Love" PRAY
You might do this to "Hello, World!" PRINT
Object that can be seen from outer space, supposedly WALL
Typical homework assignment PAPER
Setting of Flatland PLANE
Subject of estate planning WILL
Charge BILL
It might "save" you BELL
Spice that comes from a berry PEPPER
Make money MINT
LINT
Period that always begins on a Wednesday LENT
Put in a .zip file COMPRESSED
Short melody AIR
Express anger, perhaps VENT
Meeting leader, often CHAIR
Ride LIFT
It might be put away FOOD
Part of a bicycle CHAIN
Talent GIFT
What has the goods? SHOP
One's usually 2 or 3 syllables in length FOOT
Quarter of a walk BALL
GAME
It's aired SHOW
UI consideration FONT
Clog, e.g. SHOE
Leaving time? SPRING
Coward CHICKEN
Some think life originated from a type of one SOUP
Where things might get heated KITCHEN
SINK
Common data type in programming STRING
Having low pH, as a food SOUR
Fabric produced by some insects SILK
High in alcohol STRONG
Serve tea, e.g. POUR
Isolate SILO
Polynesian garment SARONG
Time for one to shine SOLO
End TIP
It's often stubbed TOE
Small amount HAIR
Something broken between competitors TIE
Low poker holding PAIR
Word on some receipts PAID
Exit LEAVE
It's sometimes represented by the peach emoji BEHIND
Feature of some cafés in Japan MAID
Primary MAIN
Song that spawned the mondegreen, "I won't chew the steak" STAY
STAG
Herbie the Love Bug's model BEETLE
Word at the end of many fortune cookie misreadings BED
Pokémon type super-effective against fire and ice ROCK
High in minerals, as water HARD
Golf action DRIVE
End counterpart, on a keyboard HOME
What some dogs do HERD
HELD
It's unlikely to freeze over HELL
Like Plan 9 from Outer Space BAD
Sight in some R-rated films BLOOD
Part of a spreadsheet CELL
Sound unit in linguistics PHONE
Song in a musical NUMBER
SPOT
Set afire LIGHT
Shallot or onion BULB
Runny liquid, at times SNOT
What some angels are made of SNOW
Part of an egg WHITE
Opposite of signal NOISE
Yellow action SLOW
Messy eater, e.g. SLOB

Within each group, the boxes and connectors form a letter shape (for most of the groups the letter is pretty clear with only the boxes, but in e.g. the fourth group, the connectors are needed to see the R shape). The groups are sorted by alphabetical order of their first clue, so we want to find a way to reorder these letters. This is where the missing pieces come in - these 20 pieces can be connected to form a big cycle, with horizontal and vertical connections working the same way as the rest of the puzzle. For example, the missing piece in the first group was CHECK with connectors on the east and west edges, which ends up joining with SPOT from the last group (connectors on the east and south edges) and BOX from the 11th group (connectors on the east and west edges).

SPOT F
CHECK I
BOX R
SEAT E
HEAD P
SHOT X
HEAT X
SINK M
HELD I
LINK E
HOLD R
LINT S
GOLD T
STAR X
PLAY X
LIST H
STAG E
PARTY R
GAME A
PLAN W

Reading the letter shapes in this cycle order, we get the words FIRE, MESH, WARE, and TRIP on the north, east, south, and west sides respectively, with Xs separating them. We can apply the connection mechanic one more time and see that WIRE makes two-word phrases with TRIP on the left side and MESH on the right side, and is one letter off of both FIRE and WARE, so this is the final answer.

Author’s Notes

The original inspiration for this puzzle came from thinking about joining word ladders via two-word phrases. This went through a lot of brainstorming, including ideas about making a 3-dimensional structure through 3 kinds of connections, or something involving counting the number of ways to navigate through a set of ladders. Eventually I settled on this extraction since it could potentially make for a satisfying do-it-again step, though it did make the puzzle larger than originally planned.

Much thanks to Jon Schneider for helping me put together the letter shapes, Jon and Brian Chen for writing a bunch of clues, and Alan Huang and Nathan Pinsker for helping write the CSS/HTML to make it look nice!