Which states have a word that uniquely identifies them? All other states have a letter shared with this word.

output.txt

ALABAMA -- cover DHNOS optionally CEFGIJKPQRTUVWXYZ
ALASKA -- cover EHMNO optionally BCDFGIJPQRTUVWXYZ
ARIZONA -- cover DEGHLMSW optionally BCFJKPQTUVXY
CALIFORNIA -- cover DEGHMSWZ optionally BJKPQTUVXY
COLORADO -- cover BEHIKN optionally FGJMPQSTUVWXYZ
CONNECTICUT -- cover AGHKMS optionally BDFJLPQRVWXYZ
DELAWARE -- cover BHNOS optionally CFGIJKMPQTUVXYZ
FLORIDA -- cover BCEHNSW optionally GJKMPQTUVXYZ
GEORGIA -- cover HLNSW optionally BCDFJKMPQTUVXYZ
HAWAII -- cover LNOST optionally BCDEFGJKMPQRUVXYZ
ILLINOIS -- cover ACEHM optionally BDFGJKPQRTUVWXYZ
INDIANA -- cover EGHKMO optionally BCFJLPQRSTUVWXYZ
IOWA -- cover EHLNS optionally BCDFGJKMPQRTUVXYZ
KANSAS -- cover EILRT optionally BCDFGHJMOPQUVWXYZ
KENTUCKY -- cover AOS optionally BDFGHIJLMPQRVWXZ
MAINE -- cover BCDGHOS optionally FJKLPQRTUVWXYZ
MARYLAND -- cover BEHIKO optionally CFGJPQSTUVWXZ
MICHIGAN -- cover BDEORSTW optionally FJKLPQUVXYZ
MISSISSIPPI -- cover ANO optionally BCDEFGHJKLQRTUVWXYZ
MISSOURI -- cover AHNP optionally BCDEFGJKLQTVWXYZ
MONTANA -- cover EHIKL optionally BCDFGJPQRSUVWXYZ
NEVADA -- cover BIKRT optionally CFGHJLMOPQSUWXYZ
NEW JERSEY -- cover AIOT optionally BCDFGHKLMPQUVXZ
NEW MEXICO -- cover AGHRST optionally BDFJKLPQUVYZ
NEW YORK -- cover AGIJT optionally BCDFHLMPQSUVXZ
NORTH DAKOTA -- cover EILMSU optionally BCFGJPQVWXYZ
OHIO -- cover AMN optionally BCDEFGJKLPQRSTUVWXYZ
OKLAHOMA -- cover BDINST optionally CEFGJPQRUVWXYZ
OREGON -- cover AITW optionally BCDFHJKLMPQSUVXYZ
PENNSYLVANIA -- cover DHKMORT optionally BCFGJQUWXZ
TENNESSEE -- cover AIOY optionally BCDFGHJKLMPQRUVWXZ
TEXAS -- cover HILNO optionally BCDFGJKMPQRUVWYZ
UTAH -- cover ILNOS optionally BCDEFGJKMPQRVWXYZ
VERMONT -- cover AGISY optionally BCDFHJKLPQUWXZ
VIRGINIA -- cover DEHKMO optionally BCFJLPQSTUWXYZ
WISCONSIN -- cover AEHLM optionally BDFGJKPQRTUVXYZ
WYOMING -- cover AEHS optionally BCDFJKLPQRTUVXZ

results.txt

Alabama -- UNSHOD, FISHPOND
Alaska -- PHENOM, MORPHINE, DEMIJOHN
Colorado -- BETHINK (unique)
Delaware -- BOHUNKS
Hawaii -- STOLEN, TEFLONS. LEPTONS, LOCKNUTS
Illinois -- MACHER, REMATCH, CHARMED, CHAMBER, PACHYDERM
Iowa -- UNHELMS, LUNCHES, LENGTHS, LYNCHERS
Kansas -- FLUORITE, DEVILTRY, BLIGHTER
Kentucky -- SOAP, SOBA, OPALS, ORGASM
Maryland -- KIBOSHES
Michigan -- BESTROWED
Mississippi -- NOVA, LOAN, WAGON
Missouri -- PHANG, PEAHEN, HAPPEN, PANACHE
Montana -- HULKIER, WHIPLIKE, FISHLIKE, CLERKSHIP, HUCKLEBERRIES
Nevada -- BRISKET
New Jersey -- PATIO, BIOTA, UTOPIA, OXTAIL
New Mexico -- DRAUGHTS, HATGUARDS
New York -- JUDGMATIC
North Dakota -- SUBLIME, MUESLIS, IMPULSE
Ohio -- MAN, NAME, DAMN, RAMEN, and of course MACKEREL
Oklahoma -- DUSTBIN, BENEDICTS, SUBDUCTING, UNDISTURBED
Oregon -- WAIT, WILDCAT, LAWSUIT
Tennessee -- OILWAY, MYOPIA, DAIMYO, OLYMPIAD
Texas -- HOLING, PHONILY, HOWLING, DOWNHILL
Utah -- LIONS, NOSILY, LOSING, VIOLINS
Vermont -- GASIFY, HIGHWAYS
Virginia -- SMOKEHOOD, HUMMOCKED
Wisconsin -- HAMLET, THERMAL, PAMPHLET, HEADLAMP
Wyoming -- SHEAR, SHADE, CHEERLEADERS


Arizona -- no words containing DEGHLMSW except MIDDLEWEIGHTS
California -- no words containing DEGHMSWZ
Connecticut -- no words containing AGHKMS that do not have i, e, or n
Florida -- no words with BCEHNSW but not a, i, or o
Georgia -- no words with HLNSW but not a, e, i, or o
Indiana -- no words with EGHKMO but not a or i (but MOTHERFUCKING deserves an honorable mention)
Maine -- no words with BCDGHOS but not e (honorable mention DOUCHEBAGS)
Pennsylvania -- no words with DHKMORT but not i (DURCHKOMPONIRT)

states_cover.py

states = ["ALABAMA", "ALASKA", "ARIZONA", "ARKANSAS", "CALIFORNIA", "COLORADO",
          "CONNECTICUT", "DELAWARE", "FLORIDA", "GEORGIA", "HAWAII",
          "IDAHO", "ILLINOIS", "INDIANA", "IOWA", "KANSAS", "KENTUCKY",
          "LOUISIANA", "MAINE", "MARYLAND", "MASSACHUSETTS", "MICHIGAN",
          "MINNESOTA", "MISSISSIPPI", "MISSOURI", "MONTANA", "NEBRASKA",
          "NEVADA", "NEW HAMPSHIRE", "NEW JERSEY", "NEW MEXICO",
          "NEW YORK", "NORTH CAROLINA", "NORTH DAKOTA", "OHIO", "OKLAHOMA",
          "OREGON", "PENNSYLVANIA", "RHODE ISLAND", "SOUTH CAROLINA",
          "SOUTH DAKOTA", "TENNESSEE", "TEXAS", "UTAH", "VERMONT",
          "VIRGINIA", "WASHINGTON", "WEST VIRGINIA", "WISCONSIN", "WYOMING"]

def no_letters_with( word ):
    return [s for s in states if not (set(s) & set(word))]

def greedy_set_cover( universe, tagged_sets ):
    if len( universe ) == 0:
        return []
    best_tag = None
    best_set = None
    best_u = None
    for (t,s) in tagged_sets:
        uncovered = len( universe.intersection( s ) )
        if best_u is None or uncovered > best_u:
            best_tag = t
            best_set = s
            best_u = uncovered

    if best_u is None:
        return [ "UNCOVERED" ]

    return [best_tag] + greedy_set_cover(
        universe.difference( best_set ),
        [(t,s) for (t,s) in tagged_sets if t != best_tag ] )

alphabet = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"

def cover_other_states( s ):
    universe = set( x for x in states if x != s )
    tagged_sets = [ (a, set( x for x in states if a in x ))
        for a in alphabet
        if a not in s ]
    return greedy_set_cover( universe, tagged_sets )

for s in states:
    cover = cover_other_states( s )
    if not "UNCOVERED" in cover:
        print( s, "-- cover", "".join( sorted( cover) ),
               "optionally",
               "".join( sorted( set(alphabet).difference( s ).difference( cover ) ) ) )