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Double Derangement Anagrams (Posted on 2007-12-05) Difficulty: 2 of 5
Many words have two or more anagrams, like 'tame' has anagrams of 'mate' and 'meat'.

The pair 'tame' and 'meat' are not only anagrams but are derangements of each other as well, having no letter occur in the same spot in both words.

Can you find a set of three words which are all derangements of each other?

See The Solution Submitted by Brian Smith    
Rating: 4.0000 (1 votes)

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Solution computer solutions | Comment 5 of 10 |

The following program reads from a file that serves as an anagram dictionary. This dictionary file has a record for each word in the regular word list, but before the word the file has the word's letters arranged alphabetically, followed by a space. For example, just around the first set of words that solve this puzzle, the following records appear:

abcep becap
abceps becaps
abcepsssu subspaces
abcepssu subspace
abcer acerb
abcer brace
abcer caber
abcerr bracer
abcerrs bracers
abcerrssttu subtracters
abcerrsttu subtracter

The program holds in an array the words that have the same anagram (in this case abcer) and finds sets of three that are mutually deranged (in this case acerb, brace and caber).

DIM word$(20)

OPEN "anagdict.txt" FOR INPUT AS #1
OPEN "dblderng.txt" FOR OUTPUT AS #2
 LINE INPUT #1, l$
 l$ = LTRIM$(RTRIM$(l$))
 ix = INSTR(l$, " ")
 a$ = LEFT$(l$, ix - 1)
 w$ = MID$(l$, ix + 1)
 IF a$ <> prevA$ THEN
   GOSUB analyze
   subs = 1
   subs = subs + 1
 word$(subs) = w$
 prevA$ = a$
GOSUB analyze


  good2 = 0
  FOR i = 1 TO subs
  FOR j = 1 TO subs
  FOR k = 1 TO subs
   good = 1
   FOR ix = 1 TO LEN(word$(i))
     IF MID$(word$(i), ix, 1) = MID$(word$(j), ix, 1) THEN good = 0: EXIT FOR
     IF MID$(word$(i), ix, 1) = MID$(word$(k), ix, 1) THEN good = 0: EXIT FOR
     IF MID$(word$(k), ix, 1) = MID$(word$(j), ix, 1) THEN good = 0: EXIT FOR
   IF good AND word$(k) > word$(j) AND word$(j) > word$(i) THEN
     PRINT word$(i), word$(j), word$(k): good2 = 1
     PRINT #2, word$(i), word$(j), word$(k): good2 = 1
  IF good2 THEN PRINT : PRINT #2,

The findings:

acerb         brace         caber
abiders       braised       sidebar
ardeb         barde         debar
adsorbing     boardings     signboard
obtainer      reobtain      taborine
botanise      niobates      obeisant
ablest        bleats        stable
ablest        stable        tables
claimer       miracle       reclaim
ceramist      matrices      scimetar
ceramist      mistrace      scimetar
cristae       raciest       stearic
restack       stacker       tackers
clasper       parcels       reclasp
canter        recant        trance
ascent        centas        stance
cares         escar         scare
caret         recta         trace
cater         recta         trace
aspic         picas         spica
ashed         deash         sadhe
ashed         heads         sadhe
aisled        deasil        ideals
deasil        ideals        sailed
aired         irade         redia
aridest       disrate       staider
armed         derma         madre
derat         rated         trade
dates         stead         tsade
estrange      grantees      sergeant
elaters       reslate       stealer
afters        faster        strafe
aligner       engrail       realign
gnarliest     reslating     triangles
alerting      integral      triangle
atingle       elating       gelatin
atingle       elating       genital
erasing       gainers       seringa
eatings       ingesta       seating
eatings       ingesta       teasing
hales         leash         sheal
horseman      menorahs      rhamnose
aliner        larine        renail
elastin       nailset       tenails
elastin       salient       tenails
entails       nailset       slainte
nailset       slainte       tenails
amines        inseam        semina
restrain      strainer      trainers
anestri       nastier       retinas
anestri       retains       stainer
nastier       retinas       stearin
lomenta       omental       telamon
estral        slater        talers
estral        staler        talers
lavers        slaver        versal
ravels        slaver        versal
ales          lase          seal
least         steal         tales
least         stela         tales
amen          mane          nema
restamp       stamper       tampers
marse         reams         smear
aspen         neaps         sneap
aspen         peans         sneap
ante          etna          neat
esparto       proteas       seaport
aper          pare          reap
prayers       respray       sprayer
asper         parse         reaps
asper         presa         reaps
asper         presa         spare
parse         reaps         spear
prase         rapes         spear
presa         rapes         spare
aspers        passer        sparse
ares          rase          sear
ares          rase          sera
arse          ears          sear
eras          rase          sera
estray        stayer        yarest
resaw         sware         wares
aver          rave          vera
ates          east          seta
ate           eat           tea
asking        gaskin        kiangs
angst         stang         tangs
ankh          hank          khan
hosta         oaths         shoat
ash           has           sha
instar        strain        trains
ask           kas           ska
asp           pas           spa
cedi          dice          iced
corselet      electors      selector
citer         recti         trice
counter       recount       trounce
cuter         recut         truce
chi           hic           ich
kitsch        schtik        thicks
engirdle      lingered      reedling
dishonest     hedonists     stonished
deil          idle          lied
enduros       resound       sounder
eringo        ignore        region
ergo          goer          ogre
horste        others        reshot
eth           het           the
imposer       promise       semipro
emit          item          mite
emit          item          time
estrin        insert        sinter
estrin        insert        trines
estrin        sinter        triens
inert         niter         trine
neist         stein         tines
prise         ripes         speir
esprit        sprite        tripes
esprit        stripe        tripes
ripest        sprite        tripes
ripest        stripe        tripes
rivets        stiver        verist
meno          nome          omen
presort       reports       sporter
poser         repos         spore
presto        respot        topers
presto        stoper        topers
estop         pesto         stope *
estop         pesto         topes *
estop         poets         stope
estop         stope         topes *
pesto         stope         topes *
overt         trove         voter
gunshot       hognuts       shotgun
ironings      nigrosin      rosining
opts          post          stop

The last set is quite good, accomplishing derangements in only four letters:


but equally good are another couple of 4-letter derangements:

emit  emit
item  item
mite  time

Unfortunately, mite and time are not derangements, so a 4-word set can't be formed with these words.

And even better, 3-letter sets:

asp  eat
pas  ate
spa  tea

There are other 3-letter-word sets, but they have words more obscure than pas.

I've looked through the sets and found only one set of four words that are mutually deranged:


and marked the sets of three taken from them with * above on the main list.


  Posted by Charlie on 2007-12-05 16:30:43
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