Problem of the Month
(October 2008)
This month we investigate the mathematics of anagrams, rearrangements of the letters of a word that are also a word.
1. Some English names for numbers can be anagrammed to other numbers. There are some trivial cases like 67 = 76 (SIXTY SEVEN = SEVENTY SIX). Then there are slightly more interesting cases like 112 = 211 (ONE HUNDRED TWELVE = TWO HUNDRED ELEVEN).
But we consider this example trivial since this still corresponds to anagramming the digits of the numbers. Also 2,010 = 10,002 (TWO THOUSAND TEN = TEN THOUSAND TWO) is trivial since it just anagrams the non-zero digits (Thanks to Claudio Baiocchi for noticing this). What non-trivial number anagrams can you find? What are the answers in other languages?
2. For each English anagram, there is a corresponding permutation of the letters. We give permutations in cycle format, so MANGO - AMONG illustrates the permutation (12)(345). This month we ask which permutations have English anagrams to illustrate them. I'm only allowing Scrabble words, those without capitalization, hyphenation, or contraction.
Apparently all permutations on 5 letters or fewer can be illustrated with an anagram. Can you find examples of them all? Apparently not all permutations on 6 letters can be illustrated with an anagram. Can you find any of the missing cases? Which permutations of 7 letters illustrate an English anagram? What are the answers in other languages?
ANSWERS
1.
Here are the smallest known non-trivial number anagrams in various languages:
Non-Trivial Number Anagrams
| Language | Anagram
| | Estonian | 29 = 81
KAKSKÜMMEND ÜHEKSA =
KAHEKSAKÜMMEND ÜKS
(Anti Sőlg)
|
| Danish | 1,210 = 8,900
EN TUSIND TO HUNDREDE TI =
OTTE TUSIND NI HUNDREDE
|
| Hungarian | 1,452 = 2,545
EZERNÉGYSZÁZÖTVENKETTÖ =
KÉTEZERÖTSZÁZNEGYVENÖT
(Attila Mártonfi, communicated by Károly Hajba)
| Esperanto | 2,010 = 20,000
DU MIL DEK =
DUDEK MIL=
| | Croatian | 2,010 = 20,000
DESET TISUCA DVA =
DVADESET TISUCA=
| | Norwegian | 5,010 = 50,000
FEMTUSEN TI =
FEMTI TUSEN
| | French | 182 = 224
CENT QUATRE VINGT DEUX =
DEUX CENT VINGT QUATRE
(Jean-Charles Meyrignac)
| Spanish | 5,007,367 = 13,176,600
CINCO MILLÓNES SIETE MIL TRESCIENTOS SESENTA Y SIETE =
TRECE MILLÓNES CIENTO SETENTA Y SEIS MIL SEISCIENTOS
(Joe DeVincentis)
| Hebrew | 8,020,001 = 11,080,000
שמונה מיליון עשרים אלף אחת =
אחת עשרה מיליון שמונים אלף
| | Portuguese | 9,012,080 = 10,098,000
NOVE MILHÃO DOZE MIL OITENTA =
DEZ MILHÃO NOVENTA E OITO MIL
| | Swedish | 10,013,501 = 15,030,100
TIO MILJON TRETTON TUSEN FEM HUNDRA EN =
FEMTON MILJON TRETTIO TUSEND EN HUNDRA
| | Italian | 10,017,338 = 13,016,837
DIECI MILIONI DICIASSETTE MILA TRECENTO TRENTOTTO =
TREDICI MILIONI SEDICIMILA OTTOCENTO TRENTASETTE
(Claudio Baiocchi)
| | English | 1,008,020,068 = 10,010,082,086
ONE BILLION EIGHT MILLION TWENTY THOUSAND SIXTY EIGHT =
TEN BILLION TEN MILLION EIGHTY TWO THOUSAND EIGHTY SIX
| | Dutch | 1,013,020,401 = 14,021,300,000
EENMILJARD DERTIENMILJOEN TWINTIGDUIZEND VIERHONDERDEEN =
VEERTIENMILJARD EENENTWINTIGMILJOEN DRIEHONDERDDUIZEND
| | | |
Jean-Charles Meyrignac supposedly found all the French number anagrams up to 1 million, and confirmed that a solution of Eric Angelini's was minimal, but then found the shorter solution above.
Attila Mártonfi found all the Hungarian number anagrams smaller than 10,000, and confirmed his solution is minimal.
The smallest anagram sum in English is 11 + 2 = 12 + 1 (ELEVEN + TWO = TWELVE + ONE). Jean-Charles Meyrignac found the smallest anagram sum in French:
345 + 221 + 215 = 592 + 156 + 32 + 1
(TROIS CENT QUARANTE CINQ + DEUX CENT VINGT ET UN + DEUX CENT QUINZE =
CINQ CENT QUATRE VINGT DOUZE + CENT CINQUANTE SIX + TRENTE DEUX + UN).
Claudio Baiocchi would change the definition of "non trivial" anagrams to exclude the rearrangement of words.
2.
The number of non-trivial permutations of length n is n!-1. Each anagram pair illustrates both a permutation and its inverse. Some permutations are their own inverse and some are not. Thus the number of permutations needed to illustrate a complete set of anagrams of length 2-7 are 1, 4, 16, 72, 397, and 2635.
Richard Sabey points out that all the permutations of 6 letters (using a very large dictionary) can be found in the book "Making the Alphabet Dance" by Ross Eckler, and in the Nov 1977 and May 1978 issues of Word Ways.
Here are the known cases of length 6 or less:
Length 2
Length 3
| Perm | Anagram
| | (12) | WON - OWN
|
| (13) | RAT - TAR
|
| (23) | EAR - ERA
|
| (123) | ONE - EON
|
Length 4
| Perm | Anagram
| | (12) | ABLE - BALE
|
| (13) | CAPE - PACE
|
| (14) | MORN - NORM
|
| (23) | BARN - BRAN
|
| (24) | GORY - GYRO
|
| (34) | COAL - COLA
|
| (12)(34) | NOSE - ONES
|
| (13)(24) | ARCH - CHAR
|
| (14)(23) | BARD - DRAB
|
| (123) | ACRE - RACE
|
| (124) | ALUM - MAUL
|
| (134) | LAMB - BALM
|
| (234) | BAKE - BEAK
|
| (1234) | AVER - RAVE
|
| (1243) | IDLE - LIED
|
| (1324) | SHAG - GASH
|
Length 5
| Perm | Anagram
| | (12) | RACED - ARCED
| | (13) | CAPES - PACES
| | (14) | MORNS - NORMS
| | (15) | SMITE - EMITS
| | (23) | BARNS - BRANS
| | (24) | STAKE - SKATE
| | (25) | SNAIL - SLAIN
| | (34) | COALS - COLAS
| | (35) | WIDER - WIRED
| | (45) | ANGEL - ANGLE
| | (12)(34) | AMENS - MANES
| | (12)(35) | NOTES - ONSET
| | (12)(45) | MOIST - OMITS
| | (13)(24) | EMITS - ITEMS
| | (13)(25) | CRUEL - ULCER
| | (13)(45) | LAPSE - PALES
| | (14)(23) | EMITS - TIMES
| | (14)(25) | SHALE - LEASH
| | (14)(35) | LASER - EARLS
| | (15)(23) | DRIES - SIRED
| | (15)(24) | STRAP - PARTS
| | (15)(34) | SONIC - COINS
| | (23)(45) | PORES - PROSE
| | (24)(35) | MERIT - MITER
| | (25)(34) | PLATE - PETAL
|
| |
| Perm | Anagram
| | (123) | ACRES - RACES
| | (124) | SITAR - ASTIR
| | (125) | TEARS - STARE
| | (134) | GROAN - ARGON
| | (135) | TIDES - SITED
| | (145) | CANED - DANCE
| | (234) | BAKES - BEAKS
| | (235) | PETAL - PLEAT
| | (245) | CADRE - CEDAR
| | (345) | LAGER - LARGE
| | (1234) | LARGE - GLARE
| | (1235) | ONSET - TONES
| | (1243) | EARLY - RELAY
| | (1245) | COINS - SCION
| | (1253) | ARGOT - GATOR
| | (1254) | REACT - CRATE
| | (1324) | COATS - TACOS
| | (1325) | DRAIN - NADIR
| | (1345) | ACRES - SCARE
| | (1354) | RINSE - SIREN
| | (1425) | SHELF - FLESH
| | (1435) | PETAL - LEAPT
| | (2345) | LAPSE - LEAPS
| | (2354) | PALER - PEARL
| | (2435) | STEAK - SKATE
|
| |
| Perm | Anagram
| | (12345) | EARTH - HEART
| | (12354) | OATHS - HOAST
| | (12435) | HARES - SHEAR
| | (12453) | LAPSE - PLEAS
| | (12534) | IDEAL - AILED
| | (12543) | REBID - BRIDE
| | (13245) | COAST - TACOS
| | (13254) | TRUCE - CUTER
| | (13425) | TREAD - DATER
| | (13524) | IDEAS - ASIDE
| | (14235) | OPTED - DEPOT
| | (14325) | CHEAT - TEACH
| | (12)(345) | MANGO - AMONG
| | (13)(245) | ONSET - STONE
| | (14)(235) | ENDOW - OWNED
| | (15)(234) | SPEAR - RAPES
| | (23)(145) | RACES - SCARE
| | (24)(135) | CEDAR - RACED
| | (25)(134) | GLARE - REGAL
| | (34)(125) | PENIS - SPINE
| | (35)(124) | LANCE - CLEAN
| | (45)(123) | LAGER - GLARE
|
|
Length 6
| Perm | Anagram
| | (12) | INCEST - NICEST
| | (13) | CARING - RACING
| | (14) | TRACES - CRATES
| | (15) | COURSE - SOURCE
| | (16) | RUSTED - DUSTER
| | (23) | CARVED - CRAVED
| | (24) | SMILED - SLIMED
| | (25) | STRIPE - SPRITE
| | (26) | GROVEL - GLOVER
| | (34) | TRAILS - TRIALS
| | (35) | INCEST - INSECT
| | (36) | WARDEN - WANDER
| | (45) | ANGELS - ANGLES
| | (46) | BURDEN - BURNED
| | (56) | SHRIEK - SHRIKE
| | (12)(34) | OPINES - PONIES
| | (12)(35) | INSECT - NICEST
| | (12)(36) | INSERT - NITERS
(Joe DeVincentis)
| (12)(45) | FAILED - AFIELD
| | (12)(46) | ?
| (12)(56) | CANOED - ACNODE
(Corey Plover)
| (13)(24) | AMBLED - BLAMED
| | (13)(25) | ASPIRE - PRAISE
| | (13)(26) | BORATE - REBATO
| | (13)(45) | DERAIL - REDIAL
| | (13)(46) | STIFLE - ITSELF
| | (13)(56) | LAMING - MALIGN
(Corey Plover)
| (14)(23) | CARTED - TRACED
| | (14)(25) | INSURE - URSINE
| | (14)(26) | MYRTLE - TERMLY
(Joe DeVincentis)
| (14)(35) | UNLIST - INSULT
| | (14)(36) | DANGER - GARDEN
| | (14)(56) | ENLIST - INLETS
| | (15)(23) | DERATS - TREADS
(Corey Plover)
| (15)(24) | REBUTS - TUBERS
| | (15)(26) | ANEMIC - ICEMAN
| | (15)(34) | THROWS - WHORTS
(Joe DeVincentis)
| (15)(36) | SHIRTY - THYRSI
(Joe DeVincentis)
| (15)(46) | CRISTA - TRIACS
(Corey Plover)
| (16)(23) | RAILED - DIALER
| | (16)(24) | SPARED - DRAPES
| | (16)(25) | SALTED - DELTAS
| | (16)(34) | DUTIES - SUITED
| | (16)(35) | ACTORS - SCROTA
(Corey Plover)
| (16)(45) | HATRED - DALETH
| | (23)(45) | CRUSTY - CURTSY
| | (23)(46) | SANDER - SNARED
| | (23)(56) | BRUISE - BURIES
| | (24)(35) | BARLEY - BLEARY
| | (24)(36) | LADING - LIGAND
(Joe DeVincentis)
| (24)(56) | SORTED - STRODE
| | (25)(34) | MAIDEN - MEDIAN
| | (25)(36) | RUSTIC - RICTUS
| | (25)(46) | PLAYER - PEARLY
| | (26)(34) | CAUDLE - CEDULA
(Corey Plover)
| (26)(35) | CLOSER - CRESOL
| | (26)(45) | ANTRES - ASTERN
(Joe DeVincentis)
| (34)(56) | RECAST - REACTS
| | (35)(46) | TEPHRA - TERAPH
(Joe DeVincentis)
| (36)(45) | PISTOL - PILOTS
| | (12)(34)(56) | ONSIDE - NOISED
| | (12)(35)(46) | ESCHAR - SEARCH
(Corey Plover)
| (12)(36)(45) | INSERT - NITRES
(Corey Plover)
| (13)(24)(56) | INFEST - FEINTS
| | (13)(25)(46) | CORSET - RECTOS
| | (13)(26)(45) | ULNARE - NEURAL
(Bojan Basic)
| (14)(23)(56) | ERUPTS - PUREST
| | (14)(25)(36) | LAYOUT - OUTLAY
| | (14)(26)(35) | TRANCE - NECTAR
| | (15)(23)(46) | ?
| (15)(24)(36) | ?
| (15)(26)(34) | ALMOST - STOMAL
(Joe DeVincentis)
| (16)(23)(45) | DOTERS - STORED
(Joe DeVincentis)
| (16)(24)(35) | TANREC - CREANT
(Bojan Basic)
| (16)(25)(34) | REPAID - DIAPER
| | (123) | RIPEST - PRIEST
| | (124) | ASCENT - SECANT
| | (125) | REACTS - TRACES
| | (126) | SPIDER - PRIDES
| | (134) | LATHER - HALTER
| | (135) | PALTRY - RAPTLY
| | (136) | BUSIER - RUBIES
| | (145) | LIFERS - RIFLES
| | (146) | WHORES - SHOWER
| | (156) | LIMPED - DIMPLE
| | (234) | BREAST - BAREST
| | (235) | TRIPOD - TORPID
| | (236) | PASTEL - PLATES
| | (245) | AUGERS - ARGUES
| | (246) | RUSTLE - RESULT
| | (256) | MANTLE - MENTAL
| | (345) | ALERTS - ALTERS
| | (346) | WANDER - WARNED
| | (356) | MOLEST - MOTELS
| | (456) | RETINA - RETAIN
| | (123)(456) | ARMING - MARGIN
| | (123)(465) | REPOST - PRESTO
(Bryce Herdt)
| (124)(356) | ?
| (124)(365) | ARIELS - RESAIL
(Corey Plover)
| (125)(346) | ?
| (125)(364) | AMINES - MESIAN
(Corey Plover)
| (126)(345) | ASCEND - DANCES
| | (126)(354) | PLAINS - SPINAL
| | (134)(256) | AIGLET - GELATI
(Corey Plover)
| (134)(265) | ASCENT - ENACTS
| | (135)(246) | RIPEST - STRIPE
| | (135)(264) | PYLORI - ROPILY
(Corey Plover)
| (136)(245) | BISTRO - ORBITS
| | (136)(254) | SLEUTH - HUSTLE
| | (145)(236) | IGNORE - REGION
| | (145)(263) | ?
| (146)(235) | FILETS - STIFLE
| | (146)(253) | AFTERS - STRAFE
| | (156)(234) | ALMOND - DOLMAN
(Corey Plover)
| (156)(243) | TAILED - DILATE
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| |
| Perm | Anagram
| | (1234) | PARSED - SPARED
| | (1235) | OCTAVE - VOCATE
| | (1236) | OUSTER - ROUTES
| | (1243) | NEURAL - UNREAL
| | (1245) | INGEST - SIGNET
| | (1246) | TRADES - STARED
| | (1253) | ACTORS - TAROCS
(Corey Plover)
| (1254) | CHASTE - SCATHE
| | (1256) | INLETS - SILENT
| | (1263) | DISOWN - INDOWS
(Corey Plover)
| (1264) | NEBULA - UNBALE
(Corey Plover)
| (1265) | ESCARP - RECAPS
(Corey Plover)
| (1324) | SLIMED - MISLED
| | (1325) | BRIEFS - FIBERS
| | (1326) | ADORES - SOARED
| | (1345) | ALINES - ELAINS
(Corey Plover)
| (1346) | ARMLET - TRAMEL
(Corey Plover)
| (1354) | WOLVES - VOWELS
| | (1356) | BAREST - TABERS
(Corey Plover)
| (1364) | FIDGIT - GIFTED
| | (1365) | WATERS - RAWEST
| | (1425) | ENLIST - SILENT
| | (1426) | IMBRUE - ERBIUM
| | (1435) | ITCHES - ETHICS
| | (1436) | LADIES - SAILED
| | (1456) | EQUALS - SQUEAL
| | (1465) | KINDLE - LINKED
| | (1526) | CHARTS - STARCH
| | (1536) | DAUBER - EARBUD
(Corey Plover)
| (1546) | RANSOM - MANORS
| | (2345) | DIVERS - DRIVES
| | (2346) | CARTEL - CLARET
| | (2354) | HATERS - HEARTS
| | (2356) | BUSIER - BRUISE
| | (2364) | PARLEY - PLAYER
| | (2365) | GIRDLE - GLIDER
| | (2456) | ONAGER - ORANGE
(Corey Plover)
| (2465) | PATHOS - POTASH
| | (2546) | PANTIE - PINETA
(Corey Plover)
| (3456) | REIGNS - RESIGN
| | (3465) | STAYED - STEADY
| | (3546) | RUSTED - RUDEST
| | (12)(345) | ADONIS - DANIOS
(Corey Plover)
| (12)(346) | ALIGNS - LASING
(Corey Plover)
| (12)(356) | AROINT - RATION
(Corey Plover)
| (12)(456) | ESCORT - SECTOR
| | (13)(245) | HOARSE - RASPED
| | (13)(246) | CHASER - ARCHES
| | (13)(256) | ?
| (13)(456) | SUBLET - BUSTLE
| | (14)(235) | MUSCLY - CLUMSY
| | (14)(236) | CASTER - TRACES
| | (14)(256) | UNITER - TRIUNE
| | (14)(356) | DONGLE - GOLDEN
(Corey Plover)
| (15)(234) | AIRBUS - URBIAS
(Corey Plover)
| (15)(236) | ARSINO - NORIAS
(Corey Plover)
| (15)(246) | DIREST - STRIDE
| | (15)(346) | PHRASE - SHERPA
(Corey Plover)
| (16)(234) | GROANS - SARONG
| | (16)(235) | SINGER - REIGNS
| | (16)(245) | ENACTS - STANCE
| | (16)(345) | BEARDS - SERDAB
(Corey Plover)
| (23)(145) | CARETS - TRACES
(Corey Plover)
| (23)(146) | PAIRED - DIAPER
| | (23)(156) | CARNET - TRANCE
(Corey Plover)
| (23)(456) | PALEST - PLATES
| | (24)(135) | CORSET - ESCORT
| | (24)(136) | CODENS - SECOND
(Corey Plover)
| (24)(156) | MELONS - SOLEMN
| | (24)(356) | PALEST - PETALS
| | (25)(134) | REMAIN - AIRMEN
| | (25)(136) | LASTED - DELTAS
| | (25)(146) | POSTED - DESPOT
| | (25)(346) | DIALER - DERAIL
| | (26)(134) | LYRATE - REALTY
(Corey Plover)
| (26)(135) | ALERTS - ESTRAL
(Corey Plover)
| (26)(145) | INSOLE - LESION
| | (26)(345) | STANCE - SECANT
| | (34)(125) | AGONES - GENOAS
(Corey Plover)
| (34)(126) | ARGUES - SAUGER
(Corey Plover)
| (34)(156) | ARPENT - TREPAN
(Corey Plover)
| (34)(256) | CAUSER - CESURA
(Corey Plover)
| (35)(124) | CANOES - OCEANS
| | (35)(126) | PRECIS - SPICER
(Corey Plover)
| (35)(146) | CHALET - THECAL
(Corey Plover)
| (35)(246) | BASTER - BREAST
| | (36)(124) | RELOAD - ORDEAL
| | (36)(125) | ENGIRD - REDING
(Corey Plover)
| (36)(145) | SENORA - REASON
| | (36)(245) | MISTER - MERITS
| | (45)(123) | LAGERS - GLARES
| | (45)(126) | ARIELS - SAILER
(Corey Plover)
| (45)(136) | BESTUD - DEBUTS
(Corey Plover)
| (45)(236) | PASTIL - PLAITS
(Corey Plover)
| (46)(123) | INBRED - BINDER
| | (46)(125) | ?
| (46)(135) | MANTLE - LAMENT
| | (46)(235) | BUSTLE - BLUEST
| | (56)(123) | RUBIES - BRUISE
| | (56)(124) | AIRMEN - MARINE
| | (56)(134) | GAMIER - MAIGRE
(Corey Plover)
| (56)(234) | FINEST - FEINTS
| | (135246) | POSTER - REPOST
(Bryce Herdt)
| (153426) | THREAD - DEARTH
(Bryce Herdt)
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
| |
| Perm | Anagram
| | (12345) | UNWARY - RUNWAY
| | (12346) | ALIENS - SALINE
| | (12354) | THROES - OTHERS
| | (12356) | SCRAPE - ESCARP
| | (12364) | PARSEC - SPACER
| | (12365) | UNRIPE - PUNIER
| | (12435) | ACORNS - NARCOS
(Corey Plover)
| (12436) | OLDIES - SOILED
| | (12453) | AIVERS - VARIES
(Corey Plover)
| (12456) | HORNET - THRONE
| | (12463) | ORCHID - RHODIC
(Corey Plover)
| (12465) | ?
| (12534) | TENSOR - STONER
| | (12536) | ITSELF - FILETS
| | (12543) | HATRED - THREAD
| | (12546) | ?
| (12563) | AORIST - RATIOS
(Corey Plover)
| (12564) | ?
| (12634) | NEBULA - UNABLE
| | (12635) | ARKOSE - RESOAK
(Corey Plover)
| (12643) | UNBRED - BURDEN
| | (12645) | ANTICK - CATKIN
(Corey Plover)
| (12653) | ASPIRE - PARIES
(Corey Plover)
| (12654) | AIMFUL - FAMULI
(Corey Plover)
| (13245) | SUNLIT - INSULT
| | (13246) | CHISEL - LICHES
(Corey Plover)
| (13254) | BRUTES - TUBERS
| | (13256) | BEARDS - SABRED
(Corey Plover)
| (13264) | GRISON - SIGNOR
(Corey Plover)
| (13265) | HASTEN - SNATHE
(Corey Plover)
| (13425) | BELONS - NOBLES
(Corey Plover)
| (13426) | ?
| (13456) | COILED - DOCILE
| | (13465) | ORPINS - PRISON
(Corey Plover)
| (13524) | BOWELS - ELBOWS
| | (13526) | CRAPES - SECPAR
(Corey Plover)
| (13546) | DUSTER - RUDEST
| | (13564) | MILNEB - NIMBLE
(Corey Plover)
| (13624) | CAPERS - ESCARP
| | (13625) | BEDLAM - AMBLED
| | (13645) | FOREST - SOFTER
| | (13654) | MISTER - TIMERS
| | (14235) | IDEALS - LADIES
| | (14236) | ORGANS - SARONG
| | (14256) | PLATES - STAPLE
| | (14265) | SCRAPE - PARSEC
| | (14325) | ARMPIT - IMPART
| | (14326) | PETALS - STAPLE
| | (14356) | KNEADS - SNAKED
| | (14365) | PHRASE - SHAPER
| | (14526) | TRIODE - EDITOR
| | (14536) | SILENT - TINSEL
| | (14625) | SEARCH - CHASER
| | (14635) | TRANCE - CRETAN
| | (15236) | HASTED - DEATHS
| | (15246) | LUSTER - RESULT
| | (15326) | EDITOR - RIOTED
| | (15346) | DANGLE - LAGEND
(Corey Plover)
| (15426) | CHANTS - SNATCH
| | (15436) | LAYMEN - NAMELY
| | (23456) | FINGER - FRINGE
| | (23465) | BARONG - BROGAN
(Corey Plover)
| (23546) | FINDER - FRIEND
| | (23564) | BLUDGE - BUGLED
(Corey Plover)
| (23645) | PISTON - POINTS
| | (23654) | BAYMEN - BYNAME
(Corey Plover)
| (24356) | CEROUS - COURSE
(Corey Plover)
| (24365) | PASTEL - PETALS
| | (24536) | SPROUT - STUPOR
| | (24635) | BLAMED - BEDLAM
| | (25346) | BARYTE - BETRAY
(Corey Plover)
| (25436) | VALINE - VEINAL
| | (1234)(56) | VOCATE - AVOCET
| | (1235)(46) | ESTRAL - STALER
(Corey Plover)
| (1236)(45) | CODERS - SCORED
(Corey Plover)
| (1243)(56) | ALMUDE - MAULED
(Corey Plover)
| (1245)(36) | ADSORB - DOBRAS
(Corey Plover)
| (1246)(35) | CAPERS - SCRAPE
| | (1253)(46) | CRUSET - RECTUS
(Corey Plover)
| (1254)(36) | CHESTY - SCYTHE
| | (1256)(34) | ENACTS - SECANT
| | (1263)(45) | INLETS - LISTEN
| | (1264)(35) | ?
| (1265)(34) | SPACER - ESCARP
| | (1324)(56) | STAPLE - PASTEL
| | (1325)(46) | BLUEST- SUBTLE
| | (1326)(45) | ARTELS - STALER
(Corey Plover)
| (1345)(26) | ALVINE - VEINAL
(Corey Plover)
| (1346)(25) | NAILED - DENIAL
| | (1354)(26) | ?
| (1356)(24) | LEMONS - SOLEMN
| | (1364)(25) | CORSET - SECTOR
| | (1365)(24) | METALS - LAMEST
| | (1425)(36) | PERILS - LISPER
| | (1426)(35) | GELANT - TANGLE
(Corey Plover)
| (1435)(26) | BELADY - DYABLE
(Corey Plover)
| (1436)(25) | ENTRAP - PARENT
| | (1456)(23) | TIMERS - SMITER
| | (1465)(23) | ?
| (1526)(34) | ALINED - DENIAL
(Corey Plover)
| (1536)(24) | ESCARP - PARSEC
| | (1546)(23) | CERIUM - UREMIC
(Corey Plover)
| (2345)(16) | ANEMIC - CINEMA
| | (2346)(15) | PRIEST - STRIPE
| | (2354)(16) | DRAPES - SPREAD
| | (2356)(14) | FILTER - TRIFLE
| | (2364)(15) | UNPILE - LINEUP
| | (2365)(14) | TORQUE - QUOTER
| | (2456)(13) | MARINE - REMAIN
| | (2465)(13) | VECTOR - COVERT
| | (2546)(13) | ?
| (3456)(12) | AMBLER - MARBLE
| | (3465)(12) | ARISTO - RATIOS
(Corey Plover)
| (3546)(12) | WORSEN - OWNERS
| | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | | |
|
Here are the known cases of switching two letters in words of length 7 or more:
Length 7 Transpositions
| Perm | Anagram
| | (12) | NUCLEAR - UNCLEAR
| | (13) | CERTIFY - RECTIFY
| | (14) | LEADING - DEALING
| | (15) | GLANCED - CLANGED
| | (16) | COMBATS - TOMBACS
(Corey Plover)
| (17) | LATCHES - SATCHEL
| | (23) | BRAKING - BARKING
| | (24) | SKATING - STAKING
| | (25) | BILTONG - BOLTING
(Corey Plover)
| (26) | ANCHORS - ARCHONS
(Corey Plover)
| (27) | SNICKET - STICKEN
(Gavin Theobald)
| (34) | BEDLAMS - BELDAMS
(Corey Plover)
| (35) | UNMATED - UNTAMED
| | (36) | WARDENS - WANDERS
| | (37) | HURTLES - HUSTLER
| | (45) | INFRACT - INFARCT
| | (46) | IMPUTES - IMPETUS
| | (47) | MISLEAD - MISDEAL
| | (56) | CITHERN - CITHREN
(Corey Plover)
| (57) | TUMBLER - TUMBREL
| | (67) | CALIBER - CALIBRE
| | | | | | |
|
Length 8 Transpositions
| Perm | Anagram
| | (12) | COHERING - OCHERING
(Corey Plover)
| (13) | BERATING - REBATING
| | (14) | COUTHIER - TOUCHIER
(Corey Plover)
| (15) | COURSING - SOURCING
| | (17) | RINGLETS - TINGLERS
(Corey Plover)
| (23) | CRAVINGS - CARVINGS
| | (24) | PLASTERY - PSALTERY
(Corey Plover)
| (25) | CUSTOMER - COSTUMER
| | (34) | COINFERS - CONIFERS
(Corey Plover)
| (35) | MOLARITY - MORALITY
(Corey Plover)
| (36) | TRAPLINE - TRIPLANE
(Corey Plover)
| (37) | CLEMATIS - CLIMATES
(Corey Plover)
| (45) | INFARCTS - INFRACTS
(Corey Plover)
| (48) | OUTRIDES - OUTSIDER
(Corey Plover)
| (56) | COMPILED - COMPLIED
| | (57) | GAMBLERS - GAMBRELS
(Corey Plover)
| (67) | QUICKEST - QUICKSET
| | (78) | BLANKETS - BLANKEST
(Corey Plover)
| | | | | | | | | | | |
|
Length 9 Transpositions
| Perm | Anagram
| | (13) | GELATIONS - LEGATIONS
(Corey Plover)
| (23) | WARSTLING - WRASTLING
(Corey Plover)
| (24) | COPULATED - CUPOLATED
(Gavin Theobald)
| (25) | COSTUMING - CUSTOMING
(Gavin Theobald)
| (36) | TRAPLINES - TRIPLANES
(Corey Plover)
| (37) | HEMATOXIC - HEXATOMIC
(Gavin Theobald)
| (45) | INFARCTED - INFRACTED
(Corey Plover)
| (49) | FLUKEWORT - FLUTEWORK
(Gavin Theobald)
| (56) | COMPILERS - COMPLIERS
(Corey Plover)
| (67) | COMPLAINT - COMPLIANT
| | (68) | OVERSLIPT - OVERSPILT
(Corey Plover)
| (89) | HARMONIES - HARMONISE
(Corey Plover)
| | | | | | | | | | |
|
Length 10 Transpositions
| Perm | Anagram
| | (13) | BOLSTERING - LOBSTERING
(Gavin Theobald)
| (14) | DORMANCIES - MORDANCIES
(Gavin Theobald)
| (23) | PERVIOUSLY - PREVIOUSLY
(Gavin Theobald)
| (79) | CHRYSOLITE - CHRYSOTILE
(Gavin Theobald)
| | | |
|
Corey Plover found all the 7, 8, and 9 letter anagrams of official Scrabble words. They are listed in excel spreadsheets here, here, and here respectively.
In 2010, Claudio Meller sent me anagrams for 2 to 5 letters in Spanish. They can be found in the text file here.
If you can extend any of these results, please
e-mail me.
Click here to go back to Math Magic. Last updated 6/6/10.