The New Sudoku Players' Forum

by **JPF** » Wed Dec 04, 2013 7:40 pm

score summary for all 7 x 7 word squares:

Hidden Text: Show

Code: Select all: Scrabble-like Scrabble points score sym. non sym. Total sym. non sym. Total 98 0 0 0 68 4 72 100 0 0 0 46 26 72 102 1 0 1 217 30 247 104 0 0 0 272 42 314 106 0 0 0 642 88 730 108 1 0 1 608 112 720 110 11 0 11 1329 210 1539 112 12 2 14 1422 266 1688 114 49 4 53 2534 346 2880 116 79 6 85 2648 468 3116 118 110 28 138 3999 736 4735 120 119 18 137 4010 750 4760 122 161 46 207 5515 1030 6545 124 186 42 228 5057 1258 6315 126 181 46 227 6590 1280 7870 128 204 46 250 6382 1388 7770 130 228 62 290 7182 1390 8572 132 249 44 293 6495 1330 7825 134 278 38 316 6981 1324 8305 136 264 34 298 6352 1176 7528 138 228 40 268 6280 1118 7398 140 188 20 208 5785 1028 6813 142 211 34 245 5860 984 6844 144 182 34 216 5155 890 6045 146 157 14 171 4747 706 5453 148 145 10 155 4196 576 4772 150 132 20 152 3842 568 4410 152 108 14 122 3357 552 3909 154 80 4 84 3050 418 3468 156 80 8 88 2651 380 3031 158 45 6 51 2218 290 2508 160 40 6 46 1966 252 2218 162 23 4 27 1607 172 1779 164 13 2 15 1270 152 1422 166 8 0 8 1174 120 1294 168 6 0 6 918 118 1036 170 6 0 6 717 74 791 172 2 0 2 565 70 635 174 7 0 7 461 34 495 176 3 0 3 343 26 369 178 3 0 3 286 14 300 180 4 0 4 222 24 246 182 1 0 1 184 20 204 184 7 0 7 159 18 177 186 6 0 6 98 14 112 188 2 0 2 69 0 69 190 0 0 0 59 2 61 192 0 0 0 66 2 68 194 0 0 0 48 0 48 196 0 0 0 32 0 32 198 0 0 0 22 0 22 200 0 0 0 10 4 14 202 0 0 0 16 0 16 204 0 0 0 11 0 11 206 0 0 0 7 0 7 208 0 0 0 3 0 3 210 0 0 0 1 0 1 212 0 0 0 1 0 1 214 0 0 0 0 0 0 216 0 0 0 2 0 2 218 0 0 0 0 0 0 220 0 0 0 2 0 2 222 0 0 0 0 0 0 224 0 0 0 2 0 2 226 0 0 0 1 0 1 228 0 0 0 0 0 0 230 0 0 0 0 0 0 232 0 0 0 0 0 0 234 0 0 0 0 0 0 236 0 0 0 0 0 0 238 0 0 0 1 0 1 3820 632 4452 125813 21880 147693

Some puzzles (sub-word squares with only one solution):

Code: Select all: . E . . . E E E . E . E . . . E . E . . E . . E . . E . . E . . E . . E . . E . . E E . E . . E . . A . A . A . A . A . A . A . A . A . A . A . A . . . . . A . . A . . A . A . . . A . A . . . A .

Code: Select all: . . . . . . . . . . . . . . . . . . . . . . . . E . . . . . E E . E . . . . . E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . A . . A . . . . . . . . . A . . . . . . . . . .

Code: Select all: B . . . . . . . E . . . . . . . C . . . . . . . A . . . . . . . U . . . . . . . S . . . . . . . E

Code: Select all: . . . . . . . . . . Z . . . . . . . . . . . Z . . . Z . . . . . . . . . . . Z . . . . . . . . . .

There are 12(2x6) one-clue minimal puzzles.
They have the main diagonal symmetry:

Code: Select all: . . . . . . V . . . . . . . . . . . . . . . . . . . . . . . . J . . . . . . . . . Z . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . J . . . . . . . . . . . . . . . . . . . . . . . . . . . X . . . . . . . . . . . . . . . . . . . . . . . . . . . . X . . . . . . . . . . . . . . . . . . . . .

JPF

by **Leren** » Thu Dec 05, 2013 7:55 am

Solutions

Code: Select all: L E G A T E E Q A B A L A H C A N A S T A D I E S E L S B L U E C A P E S P A R T O E Y E B E A M A P A D A N A A L U M N U S I N C O N I E L E P T O M E S E I Z E R S G E N E T T E B A R A C A N N A T R O N S S T O U T E N U P C H E E R P I L O T I S A B E T T E R A D A P T E D A S T E R I A C O L L A R D E T H A N A L A Z O T I Z E T E T T E R S L A C T A M S S K E E T E R A N O D Y N E C O E N U R I R E T I N O L E A T E R I E A N A E M I A T A R T E S T R E G A L E R A M E A R S T T R I Z O N E E M E R S E D H A N D S A W A S S A R T S D R Y N E S S P E R L I T E O S S E L E T I S O G R I V R E R E M A I S T E A D E D P A L A B R A I S T H M U S R H A B D O M S E R R A T E E V E J A R S T E N D E N Z A T O P I E S S P H A E R E H E L L U V A O R R A M E N R E V E R S O E N T E N T E L O V A G E S T H E M A T A A L T E R E R G R A V U R E E J E C T E D A D E P T E R A P A R E J O H A M S T E R B L E W A R T R A M U L A R M A R T I N I D E N T U R E B I G E N E R M E A T A X E D U R A B L E I T E R A T E A R S E N I C E N T E R O N R E E J E C T U R T E X T S O V E R L A X V E N E R E R I S O D I C A D Z E R E N S A S S O R T S S E A R E S T M A R T E X T

Leren

by **JPF** » Thu Dec 05, 2013 12:00 pm

Congratulations!

As a reward, here is a sample of "real" non-symmetric word squares (all words in a word square are different):

Code: Select all: A C H I E V E B E N A M E D C A S C A D E D E P A R T S T R O M P E S A L A N I N E A C H A R Y A E S O T E R Y T O R P I D S G A N G S T A F E E R I E S X E R O T I C R O S A C E A S P O O M E D I R A T E S T T R O M I N O A N I L I T Y F I B R A T E L O R E T T E R I S I N G S C E L E S T E U N E A T E N A L E R T E R A N I S O L E T R Y S T E D L E S S E E S S A R S A R S N E S T L E S E T A T I S M F A S C I S M G A T E M A N H O T P O T S M U L A T T O I N C O N N U A N O L Y T E O V E R T O P B R I B E R S R E A L T E R S T R E T T A B E N E A T H R A D O M E S E M M E W E D P I T C H E R B R A W L I E A C A R I N E P O E T I Z E E G O T I S E L U C I G E N I O D I S E R O N L I N E R R E N E S T S E S E R I N E D U E N E S S T E S T E R S S N I D E S T R E S E A T S I M P R E S S J U R I S T S L E A S I N G M A S S A G E M I L I T I A A N E S T R A A L I E N E R A N A T M A N P L A C I N G C A P O R A L N A R C O M A R E V U I S T A L S O O N E A L I M E N T O P P O S E D A M A N D L A L I T T L I N M I N E T T E L I O N I S E B O N N I E S E M E T I N E A V E R T E R I N S A N E R I N T E N S E S E R A N G S R E D E A R S N E T L E S S S E E R E S S N E A T E S T P L A S T I C Q U A C K E R R E S U M E S U N B R A C E R O U T I N E U N S H A L E E M O T I V E T R A I T O R E R R A N D S E M P A R E S M A R I N E R M A N G E R S A R A B L E S L A I R A G E A N E L I N G E N D O R S E S E T L I N E E R R A T I C R A D I A T E A G O N I E S S L E E K E R A R I D E S T K N I T T E R T E N S E S T E L D R E S S S Y N E S E S S T A Y E R S S N A P P E R T R I C E P S U P R I S E R V I S T A E D T E R R E N E E O S I N I C P R E S A G E I N T E R N E E U M O N G S A B O R T E R D E M O T E S S C Y T A L E A R I S T A E S I N C E R E I D O L I S T C O L O B I D M I N T A G E E N O U N C E V I T I A T E U N I T I V E E N G I N E D L I M I T E D E V E N T E R M I N U S E S D E S E E D S S A E T E R S D E S E E D S S E G M E N T W I M B L E S A M O R A N T S P L A S H Y T R O C H A L R E S H I N E E S S E N C E L A I S S E S

JPF

by **Leren** » Fri Dec 06, 2013 11:30 am

Hi JPF, can you find any non-symmetric Scrabble 7 x 7 Word squares ?

Leren

by **JPF** » Fri Dec 06, 2013 3:08 pm

Hi Leren,

You wrote:can you find any non-symmetric Scrabble 7 x 7 Word squares ?

Here is the list - 632 non-symmetric Scrabble 7 x 7 word squares - sorted by score:

Hidden Text: Show

Code: Select all: vampingadornermozettaprelatyintaglinettlesgreyish 164 vampingadornermozetteprelatyintaglinettlesgrayish 164 campingadornermozettaprelatyintaglinettlesgreyish 162 campingadornermozetteprelatyintaglinettlesgrayish 162 watchedamaronetaberdscreminihorizonendnoteresined 162 watcheramaronetaberdscreminihorizonendnotedesined 162 batchedamaronetaberdscreminihorizonendnoteresined 160 batcheramaronetaberdscreminihorizonendnotedesined 160 dampingadornermozettaprelatyintaglinettlesgreyish 160 dampingadornermozetteprelatyintaglinettlesgrayish 160 patchedamaronetaberdscreminihorizonendnoteresined 160 patcheramaronetaberdscreminihorizonendnotedesined 160 lampingadornermozettaprelatyintaglinettlesgreyish 158 lampingadornermozetteprelatyintaglinettlesgrayish 158 rampingadornermozettaprelatyintaglinettlesgreyish 158 rampingadornermozetteprelatyintaglinettlesgrayish 158 watchedabalonetabardsclarinihorizonendnoteresined 158 watcherabalonetabardsclarinihorizonendnotedesined 158 champachavartiurinatefiddlerfairingententerayless 156 chufferharianaaviditymandrelpralineattentscierges 156 matchedabalonetabardsclarinihorizonendnoteresined 156 matcherabalonetabardsclarinihorizonendnotedesined 156 morchasoverallreveriecreakedharmingalieneesledged 156 morchasoverallreveriecreamedharkingalieneesledged 156 patchedabalonetabardsclarinihorizonendnoteresined 156 patcherabalonetabardsclarinihorizonendnotedesined 156 jostleduterinesawingstriperylinemanengravedesyned 154 justledotarinesewingstriperylinemanengravedesyned 154 morchasoverallreveriecreakedharmingalieneesledges 154 morchasoverallreveriecreamedharkingalieneesledges 154 belatedepigenerizardsagapeicterebraendirondescant 152 beratedepigenelizardsagapeicterebraendirondescant 152 hambledazurinemutandabraggedlinguaeendearssearest 152 hamblesazurinemutandabraggerlinguaeendearsdeadest 152 jostleduterinesawingstriperylinemanengracedesyned 152 justledotarinesewingstriperylinemanengracedesyned 152 kittlerigarapetaxitictriremelatenedepimereseceded 152 kittlerigarapetaxitictrisemelatenedepimereseceded 152 kittlesigarapetaxitictriremelatenedepimerereceded 152 kittlesigarapetaxitictrisemelatenedepimerereceded 152 overagevenisonendopodriotiseaspidiawoozierendears 152 overawevenisonendopodriotizeaspidiagoosierendears 152 wambledazurinemutandabraggedlinguaeendearssearest 152 wamblesazurinemutandabraggerlinguaeendearsdeadest 152 acaterscabinedabomasatimothyenationreshonestayned 150 acaterscabinetabomasatimothyenationreshonesdayned 150 banalerobovatenametagexarateyidakiselegistreseats 150 boneyerabaxilenomadesaveragelatakiaetatistregests 150 defamedenolaseforintsalizarimanagerestreperesided 150 defamerenolaseforintsalizarimanagedestrepedesired 150 dodgemsovernewdebaclegranitaencinalmeltagesweeled 150 dodgemsovernewdebaclegraniteencinalmeltageswealed 150 hambledazurinemutandabraggerlinguaeendearssearest 150 hamblesazurinemutandabraggerlinguaeendearsdearest 150 kittlerigarapetaxitictriremelatenedepimeresecedes 150 kittlerigarapetaxitictrisemelatenedepimeresecedes 150 kittlesigarapetaxitictriremelatenedepimererecedes 150 kittlesigarapetaxitictrisemelatenedepimererecedes 150 sneezernoisomeindenesphoratepoliticeminentrecedes 150 snippernonhomeeidoliceserinezonatedemetineresects 150 torpidsoversetreticlepritheeischialdeleavesweeled 150 torpidsoversewreticlepritheeischialdeleavesteeled 150 wambledazurinemutandabraggerlinguaeendearssearest 150 wamblesazurinemutandabraggerlinguaeendearsdearest 150 defamedenolaseforintsalizarimanagerestreperesider 148 defamerenolaseforintsalizarimanagedestrepedesirer 148 fetchesoveraterequirecrueleranilinetellensstayres 148 forcatsevernettequilacruellyhailieretrenneseeress 148 hobbleroverusetenacesprewireotalgictotientsphenes 148 hotpotsovertopbeneathbrawlielucigeneserineresects 148 jabbledotarinestringsturneryleadmanenclavesteened 148 jostlesattuentbarracebrindlelinemanengravedesyned 148 scrapeselementreforgeamokuraperusalengraftstealth 148 serapesclementreforgeamokuraperusalengraftstealth 148 cobbleroverusemenacesprewireotalgiatotientsphenes 146 compotsovertopbeneathbrawlielucigeneserinereseats 146 customsupthrewstrodlethoriteordinalmeltagesweered 146 customsupthrewstrodlethoriteordinarmeltagesweeled 146 gambledazurinemutantsbravuralinuronentroldresends 146 gamblerazurinemutantsbravurelinuronentrolddesands 146 jumbleruterineseringatrisulslinkrotenglobedesyned 146 justleduterinemeringsbrisklylinuronenglobereasted 146 patamaravaricetapisesariettamistbowacetoneresewed 146 patamaravaricetapisesariettemistbowacetoneresawed 146 rambledazurinemutandabraggedlinguaeendearssearest 146 ramblesazurinemutandabraggerlinguaeendearsdeadest 146 torpidsovernetrejoiceprostieinitialdeciaresweeled 146 torpidsovernewrejoiceprostieinitialdeciaresteeled 146 bagwashaureliagreetedweekendalternesiennashardest 144 bagwashaureliagreeterweekendalternesiennashaddest 144 deriderexamineraupatuimpalervialingententereurged 144 deriverexamineraupatuimpalerdialingententereurged 144 dodgemsovernetdebaclegranitaencinalmeltageswealed 144 dodgemsovernetdebaclegranitaencinalmeltagesweeled 144 dodgemsovernetdebaclegraniteencinalmeltageswealed 144 dodgemsovernetdebaclegraniteencinalmeltagesweeled 144 dodgemsovernewdebaclegranitaencinalmeltagestealed 144 dodgemsovernewdebaclegranitaencinalmeltagesteeled 144 dodgemsovernewdebaclegraniteencinalmeltagestealed 144 dodgemsovernewdebaclegraniteencinalmeltagesteeled 144 fabbieraureoletroddenteatimeiodizeselementrenests 144 fattieraureolebroadenbedtimeiodizeselementrenests 144 garbledacarineracinosgriselylinkmanenolasedesyned 144 gargledacarineracinosbrisklylinemanenolasedesyned 144 hobbleroverusetenacesprewireotalgiatotientsphenes 144 hotpotsovertopbeneathbrawlielucigeneserinereseats 144 littlerigarapetaxitictriremelatenedepimereseceded 144 littlerigarapetaxitictrisemelatenedepimereseceded 144 littlesigarapetaxitictriremelatenedepimerereceded 144 littlesigarapetaxitictrisemelatenedepimerereceded 144 rambledazurinemutandabraggerlinguaeendearssearest 144 ramblesazurinemutandabraggerlinguaeendearsdearest 144 scrapeselementreforgeamokuraperusalengravestealed 144 scrapeselementregorgeamokuraperusalengraftstealth 144 seethedestroneetourditrucinghorizonendnotereigned 144 seetherestroneetourditrucinghorizonendnotedeigned 144 serapesclementreforgeamokuraperusalengravestealed 144 serapesclementregorgeamokuraperusalengraftstealth 144 teethedestroneetourditrucinghorizonendnotereigned 144 teetherestroneetourditrucinghorizonendnotedeigned 144 whidderhemiolaimpalesdialectdolenteenactorresters 144 whidderhemioneimpalasdialectdolenteelectorrasters 144 brahmanrelievealteredhielandmerantiaventrenoddier 142 brahmanrelievealteredhielandmerantiaventrenoddies 142 brahmanrelievealteredhielandmerantiaventresoddier 142 brahmanrelievealteredhielandmerantiaventresoddies 142 brahmanrelievoalteredhielandmerantiaventreneddier 142 brahmanrelievoalteredhielandmerantiaventreneddies 142 brahmanrelievoalteredhielandmerantiaventresoddier 142 brahmanrelievoalteredhielandmerantiaventresoddies 142 brahmanrilievoalteredhielandmerantiaventresoddier 142 brahmanrilievoalteredhielandmerantiaventresoddies 142 brahmasrelievoalteredhielandmerantiaventreneddier 142 brahmasrelievoalteredhielandmerantiaventreneddies 142 brahmasrelievoalteredhielandmerantiaventrenoddier 142 brahmasrelievoalteredhielandmerantiaventrenoddies 142 brahmasrilievoalteredhielandmerantiaventrenoddier 142 brahmasrilievoalteredhielandmerantiaventrenoddies 142 caperedoveragepesetaserectlyrattlinegalitedesyned 142 coperedaveragepesetaserectlyrattlinegalitedesyned 142 deriderexamineraupatuimpalervialingententereurges 142 deriverexamineraupatuimpalerdialingententereurges 142 littlerigarapetaxitictriremelatenedepimeresecedes 142 littlerigarapetaxitictrisemelatenedepimeresecedes 142 littlesigarapetaxitictriremelatenedepimererecedes 142 littlesigarapetaxitictrisemelatenedepimererecedes 142 morularozoniderosacesunadeptlicenteadepterseaters 142 morulasozoniderosaceaunadeptlicenteadepterresters 142 scrapeselementreforgeamokuraperusalengracestealed 142 serapesclementreforgeamokuraperusalengracestealed 142 strobictheretoresidedorigamibedawiniteminglorings 142 strobictheretoresidedorigamibedawiniteminglosings 142 strobiltheretoresiderorigamibedawinitemingcodings 142 strobiltheretoresidesorigamibedawinitemingcodings 142 torpidsovernetretitlepritheeinthraldeleavesweeled 142 torpidsovernewretitlepritheeinthraldeleavesteeled 142 adapterdeceiveachatespeasanttitaniaoveningrestage 140 adaptordeceiveachatespeasanttitaniaeveningrestage 140 caperedoveragepesetaserectlyrattlinegalitedesynes 140 coperedaveragepesetaserectlyrattlinegalitedesynes 140 heptadsexurbiapunaanitrantedabaturedinerossairest 140 heptadsexurbiapunaanitranterabaturedinerossaidest 140 satrapsephoralboroniaalimonycuvetteinertercensors 140 scrapeselementregorgeamokuraperusalengravestealed 140 scrutoschalonerevelerulexitetolidinonetimeserened 140 scrutoscheloneravelerulexitetolidinonetimeserened 140 sebacicapolunethrivenroomersarnottopainterslayers 140 seethedestroneetourditrueinghorizonendnotereigned 140 seetherestroneetourditrueinghorizonendnotedeigned 140 serapesclementregorgeamokuraperusalengravestealed 140 sprawlstravailreverseupendedmuntingacerateserened 140 strumasprepuceraveneraventrewardianlisentesledged 140 teethedestroneetourditrueinghorizonendnotereigned 140 teetherestroneetourditrueinghorizonendnotedeigned 140 vodcastoleariadealerscanzoneareolarsirnametasered 140 vodcastoleariadeanerscalzoneareolarsirnametasered 140 acromiachivariripenedoverallmanateeirelessairless 138 acromiachivariripeneroverallmanateeirelessaidless 138 caraculanemonereversiemendedfordingunsenseleidger 138 carefulanemonereversiamendedcordingunsenseleidger 138 dodgemsovernetdebaclegranitaencinalmeltagesteeled 138 dodgemsovernetdebaclegraniteencinalmeltagestealed 138 empaledmauvinepudendaavengerlinguaeendearssearest 138 empalesmauvinepudendaavengerlinguaeendearsdearest 138 halberdawaiterlairagebiremesetaminsregencetressed 138 halbertawaiterlairagebiremesetaminsregencedressed 138 humbleruterineseringatrisulslinkrotenglobedesyned 138 hustleduterinemeringsbrisklylinuronenglobereasted 138 impaledmauvinepudendaavengerlinguaeendearssearest 138 impalesmauvinepudendaavengerlinguaeendearsdearest 138 podcastoleariadealerscanzoneareolarsirnametasered 138 podcastoleariadeanerscalzoneareolarsirnametasered 138 scrapeselementregorgeamokuraperusalengracestealed 138 scrutoschalonerevelerulexitetolidinonetimeserener 138 scrutoschalonerevelerulexitetolidinonetimeserenes 138 scrutoscheloneravelerulexitetolidinonetimeserener 138 scrutoscheloneravelerulexitetolidinonetimeserenes 138 seawardescapeeacerolawarbledapolunerelendsdearest 138 seawardescapeeacerolawarblerapolunerelendsdeadest 138 serapesclementregorgeamokuraperusalengracestealed 138 shedderhemioneimpalasdialectdolenteelectorrasters 138 shidderhemiolaempalesdialectdolenteenactorresters 138 shidderhemiolaimpalesdialectdolenteenactorresters 138 shidderhemioneimpalasdialectdolenteelectorrasters 138 stratasurediumnedettewarehouatomicsrevenuedredges 138 sunwardtreaterredroveadeemedtithingautocuesmeuses 138 tombocsovernetmegillabrinierowliestcelestestarted 138 tombocsoverwetmegillabrinieronliestcelestestarted 138 torpidsovernetrevoiceprostieinitialdeciaresweeled 138 torpidsovernewrevoiceprostieinitialdeciaresteeled 138 trampedrevoiceavellanmolderspileateecartestensest 138 trampetrevoiceavellanmolderspileateecartesdensest 138 trouledrepriveoptimesuridinelymiterevenestdeserts 138 trouledrepryveoptimesuridinelimiterevenestdeserts 138 yardarmalieneerichensdehornsanergiarentingmessage 138 yardarmalieneerichensdehortsanergiarenningmessage 138 campledacarinemadonnaproggedlinguaeenneadssearest 136 camplesacarinemadonnaproggerlinguaeenneadsdeadest 136 defacedepidotefilariaadaptorcortilietiolinrearing 136 defacedepidotefilariaadaptorcortilietiolinsearing 136 defacerepidotefilariaadaptorcortilietiolindearing 136 defacesepidotefilariaadaptorcortilietiolindearing 136 dodgemsoverlitdejeunegreaserelutionmineolasternal 136 dodgemsoverlitdejeunegreaterelusionmineolasternal 136 incomerniobatecoronalobovatemanakinetatistresents 136 incomerniobatecoronasobovatemanakinetatistrelents 136 laciestaginnerkitharainhumedenamineserenertraders 136 lakiestaginnercitharainhumedenamineserenertraders 136 longansovernetnedettegreciseantifurnetsukesweered 136 longansovernewnedettegreciseantifurnetsukesteered 136 paradoralewiferetasteawaitedmistuneoftenerseeders 136 paramosalewiferetasteawaiteddistuneoftenerreeders 136 reboredexaratebataviaorarionraviolietiolinseaning 136 reboredexaratebataviaorationraviolietiolinseaning 136 reboresexaratebataviaorarionraviolietiolindeaning 136 reboresexaratebataviaorationraviolietiolindeaning 136 seawardescapeeacerolawarbledapolunerelentsdearest 136 seawardescapeeacerolawarblerapolunerelentsdeadest 136 strobiltheretoresiderorigamibedawiniteminglosings 136 strobiltheretoresidesorigamibedawiniteminglorings 136 tombocsovernetmegillabrinierowliestcelestestarter 136 tombocsoverwetmegillabrinieronliestcelestestarter 136 trampedrevoiceavellanmolterspileateecartestensest 136 trampetrevoiceavellanmolterspileateecartesdensest 136 wastrelachieveshortentitlingretireeevenerslengest 136 wastrelachieveshottentirlingretireeevenerslengest 136 whatsithemioneamanitatinklersoilageintegerteasers 136 whatsithemioneamanitatinklessoilageintegertearers 136 zestierententestrafedteawareinfaunaeternalreseals 136 zestierententestrafesteawareinfaunaeternalredeals 136 campledacarinemadonnaproggerlinguaeenneadssearest 134 camplesacarinemadonnaproggerlinguaeenneadsdearest 134 castralachieveshortentitlingretinueavenueslengest 134 castralachieveshottentirlingretinueavenueslengest 134 clampedligularaggratemuricesplanerseateriedressed 134 clampedligularaggratemurinesplacerseateriedressed 134 compendoverseanegatorcratingestivalneonatetangles 134 concentoverseamegatonpratingestivalneonatedargles 134 defacerepidotefilariaadaptorcortilietiolinsearing 134 defacesepidotefilariaadaptorcortilietiolinrearing 134 elapidsleveretavariceperidiairidialdeciaresteanes 134 elapidsleveretavariceperidiairidiandeciaresteales 134 factoidamaronecanastatrampedoosporeinternsdearest 134 factoidamaronecanastatramperoosporeinternsdeadest 134 factoidamaronecatastatrampedoosporeinternsdearest 134 factoidamaronecatastatramperoosporeinternsdeadest 134 greaserrampireembolicapolunesilurideriniteseceded 134 greasesrampireembolicapolunesiluriderinitereceded 134 hatsfularrieretruemansievingfeminieuraniaslongest 134 hatsfularrieretruemansievingfeminieuraninslongest 134 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malicesamaronelavoltaironiercolibrienterondearing 128 malicesamaronelavoltaironiescolibrienterondearing 128 matcheropalinestrettasedatereriniteravenersledges 128 mossersapteraltardivecleanedhittingenteteerearers 128 negatedepimeregironicamorinitenioideriniterecodes 128 negatedepimeregironicamorinotenioideriniterecodes 128 negaterepimeregironicamorinotenioiderinitedecides 128 negaterepimeregironicamorinotenioiderinitedecodes 128 patcheropalinestrettasedatereriniteravenersledges 128 possersapteraltardivecleanedhittingenteteerearers 128 proctorreshoneosmolalcholinetolidinonanistrerents 128 proctorreshoneosmolalchorinetolidinonanistrerents 128 proctorreshoneosmolarcholinetolidinonanistrelents 128 proctorreshoneosmolarchorinetolidinonanistrelents 128 rabideracerolabevomitironisedominieelisionrattens 128 rabideracerolabevomitironistdominieelisionrateens 128 ratchedopalinestrettasedatederiniteravenersledges 128 rossersapteraltardivecleanedhittingenteteedeaders 128 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epigenesenopiacronetsrosiereiridialbatisteelected 124 escribeperoralinositegonidicepeeistnitrateeaseled 124 gloatedlabroseobversearettedtortoniessencereedier 124 gloaterlabroseobversearettedtortoniessencedeedier 124 hirpledisolinerotundapluggerlinguaeendearssearest 124 hirpledisolinerotundaplungedlinguaeendearssearest 124 hirplesisolinerotundapluggerlinguaeendearsdearest 124 hirplesisolinerotundaplungerlinguaeendearsdeadest 124 kirtlediterateretinastrisomylanolinenaminesteened 124 kirtlesiterantretinaetrisomelanolinetaminedesyned 124 modularoperaterefectsurediallaciniaattaintreslate 124 morularoperatedefectsurediallaciniaattaintreslate 124 outraveuraemiatailersrevengeomentalairdaterassled 124 outroaruraemiataiversrelendsamentalvirgateeaseled 124 redateseminentdivergeanestratertialengravesteaned 124 redateseminentdivergeanestratertialengravesteined 124 redateseminentdivergeanestratertianengravestealed 124 redateseminentdivergeanestratertianengravesteined 124 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salicetamaronelavoltaironiercolibrienteronsearing 122 salicetamaronelavoltaironiercolibrienteronseasing 122 salicetamaronelavoltaironiercolibrienteronteasing 122 salicetamaronelavoltaironiescolibrienteronsearing 122 salicetamaronelavoltaironiescolibrienteronseasing 122 salicetamaronelavoltaironiescolibrienterontearing 122 sedateseminentdivergeanestratertialengracesteaned 122 sedateseminentdivergeanestratertialengracesteined 122 sedateseminentdivergeanestratertianengracestealed 122 sedateseminentdivergeanestratertianengracesteined 122 sedateseminentdivergeanestritertianengracestealed 122 sedateseminentdivergeanestritertianengracesteaned 122 trampedregularagitatemutinesplanerseaterietressed 122 trampetregularagitatemutinesplanerseateriedressed 122 velatedeboniselomentaanestritintierestrepedesired 122 velatedeboniselomentsanestritintierestrepedeaired 122 actuatecoarsentalipeduridineaspidiateenierensears 120 actuatecoarsentalipesuridineaspidiateenierendears 120 belatedeboniselomentaanestritintierestrepedesired 120 belatedeboniselomentsanestritintierestrepedeaired 120 lorimeroperatereginalirisatemanakinetatistresents 120 lorimeroperatereginasirisatemanakinetatistrelents 120 redateseminentdivergeanestratertialengracesteanes 120 redateseminentdivergeanestratertianengracesteales 120 relatedebonisemomentaanestritintierestrepedeaired 120 relatedebonisemomentaanestritintierestrepedesired 120 relatedebonisemomentsanestritintierestrepedeaired 120 rematedeboniselomentaanestritintierestrepedeaired 120 rematedeboniselomentaanestritintierestrepedesired 120 rematedeboniselomentsanestritintierestrepedeaired 120 tubularuranidemananasunadeptlineateadapterresters 120 tubularuranidemananasunadeptlineateadaptorresters 120 tumularuranidebananasunadeptlineateadapterresters 120 tumularuranidebananasunadeptlineateadaptorresters 120 albergolootersboragesetamineretinalgrenadeosselet 118 albergolootersboratesetaminereginalgrenadeosselet 118 alcadesrealestcavettoaleurondetrainestoilestonned 118 arcadeslealestcavettoaleurondetrainestoilestonned 118 delatedeboniselomentaanestritintierestrepedesired 118 delatedeboniselomentsanestritintierestrepedeaired 118 dilatediconiselomentaanestritintierestrepedesired 118 dilatediconiselomentsanestritintierestrepedeaired 118 epimereperidotironiseminstereditionroseolasternal 118 epimereperidotironiseminutereditionroseolasternal 118 epimersperidotironiseminstereditionroseolaeternal 118 epimersperidotironiseminutereditionroseolaeternal 118 gelatedeboniselomentaanestritintierestrepedesired 118 gelatedeboniselomentsanestritintierestrepedeaired 118 pacableaeolianrosiersaliundebiennialardierensears 118 palatedadoniselomentaanestritintierestrepedesired 118 palatedadoniselomentsanestritintierestrepedeaired 118 palatedagoniselomentaanestritintierestrepedesired 118 palatedagoniselomentsanestritintierestrepedeaired 118 parableaeoliancosiersaliundebiennialardierensears 118 radulararenitedeploreunlinedlionismatresiaseedman 118 radulasarenitedeploreunlinedlionismatresiareedman 118 restierententestrafedteawareinfaunaeternalreseals 118 restierententestrafesteawareinfaunaeternalredeals 118 sapotesamarantpontileortolantailardenlargestended 118 sapotesamorantpantileortolantailardenlargestended 118 tumbreluterinemedusaebrulotsrisoriienationlensing 118 tumbreluterinemedusanbrulotsrisoriienationleesing 118 locaterodonatecoheredanestritartanaeternalserials 116 locaterodonatecoveredanestritartanaeternalserials 116 locatesodonatecohereranestritartanaeternalredials 116 locatesodonatecovereranestritartanaeternalredials 116 relatedeboniselomentaanestritintierestrepedesired 116 relatedeboniselomentsanestritintierestrepedeaired 116 dilatedironiselomentaanestritintierestrepedesired 114 dilatedironiselomentsanestritintierestrepedeaired 114 redtopsecuellethereatretrainalternetooniesensears 114 retrateechelonduettosterreneoleariaplainersetness 114 onlinernoisomelitotesisolatenotitiaeminentrecedes 112 onlinernoisomelitoticisolinenotatedemetinereseats 112

JPF

by **Leren** » Sat Dec 07, 2013 12:30 am

Hi JPF,

I've checked your list of non-symmetric Scrabble-like 7 x 7 Word squares to see if any of them is a Scrabble Word square ie constructible in a Scrabble game. Unfortunately I can't prove that any of them has this property.

This doesn't necessarily mean that they can't be constructed, it just means that I haven't found a way to do it. The two symmetric Scrabble 7 x 7 Word squares remain the only 2 that I've found.

Leren

by **David P Bird** » Sat Dec 07, 2013 10:57 pm

JPF, Leren

Have either of you considered making a Pareto analysis of the distribution of the words that appear in your different size word squares?

I idly wondered if any words with three consecutive vowels or consonants ever appeared in any of the squares you've found. This then led me on to think about the typical situation in warehousing where 80% of the orders are satisfied by 20% of the stock items.

With little idea about how your search methods work, I can't say whether gaining this sort of knowledge would allow you to optimise your code in any way though.

In a somewhat similar vein, we have a TV program called 'Countdown' where two competitors try to find the longest words that can be constructed out of a selection of 9 letter tiles in 30 seconds. Because of the frequency distribution of the letters, certain words seem to occur quite frequently and are greeted as old favourites when they arise. One such is 'leotard', but I can't remember the others. Certainly the resident guru and adjudicator on the show recognises these almost instantaneously when the tiles are revealed.

David

by **Leren** » Sun Dec 08, 2013 5:39 am

David P Bird wrote : With little idea about how your search methods work, I can't say whether gaining this sort of knowledge would allow you to optimise your code in any way though.

Hi David and JPF,

Basically I used this method to optimise my puzzle solving attempts but I carried it out to the Nth degree. If you consider the hardest of JPF's 7 x 7 puzzles you can calculate that there are 33274 x 33274 x 33274 x 2851 x 1779 x 2468 x 33274 ~ 1.5 x 10^28 combinations of 7 words to be checked. Assuming I was able to try 10,000,000 combinations/sec (an optimistic estimate - my desktop can count up to about 100,000,000 in 1 sec) it would take ~ 50, 000, 000, 000, 000 years to check all combinations ! I managed to get this down to under 2 hours for this puzzle.

The trick I used was to convert the entire dictionary letter by letter into the numbers 1 - 26 and use a series of boolean arrays and base 27 arithmetic to record whether at least one word with a particular letter sequence was in the dictionary. So, for example Allowed123 (1 + 27 * 1 + 729 * 18) is True because there is a word with AAR in the first three letters, but Allowed123(1 + 27 * 1 + 729 * 19) is False because there is no word with AAT in the first 3 letters. I also created arrays that determined where the next letter position was in the dictionary. This enabled me to skip over most row combinations. So, for example, if I were to test

Code: Select all: AARRGHH ABACTOR ABALONE

I'd immediately find that AAA in Column 1 was false and quickly skip down to

Code: Select all: AARRGHH ABACTOR RABANNA

(In practice RC in column 4 is also invalid, so I would have skipped ABACTOR using and Allowed12 array, but I think you should get the idea from this example).

The computational cost of determining the Boolean arrays is small - of the order of k x 33274, where k is a small number. Unfortunately Visual Basic only allowed me to create Boolean arrays to test up to 5 letter positions (due to a size limitation), so I actually had to occasionally test whether vertical 7 letter combinations were actually in the dictionary. Since the dictionary is well ordered the computational cost of this is ~ k1 x log 2 (33274).

Checking symmetric Word squares is very fast because the same letter combinations must appear in each corresponding row/column, which reduces the computational cost by ~ 33274.

I hope this has been of interest.

Leren

by **David P Bird** » Sun Dec 08, 2013 10:05 am

Leren, many thanks for your interesting and enlightening response – all that is very clever!

Pareto analysis aims to optimise the efficiency of the bulk of the work. In the context of 7-letter word squares I'd guess that there is most freedom of choice for the first and last letters in a word. If so, the most restrictive positions are those that make the central 5x5 array of letters. Although counter-intuitive, this would suggest that the 5 positions to be binary coded and sorted should be for positions 2 to 6. Once a candidate 5x5 core array had been found (the bulk work), then a search would be made for the available words to top and tail the rows and columns where there may be several options.

On the basis that 'if it ain't broke don't fix it', I'm not suggesting that you should re-write your code though. It's just my armchair reaction to your description.

David

by **JPF** » Sun Dec 08, 2013 10:56 am

David wrote:we have a TV program called 'Countdown' where two competitors try to find the longest words that can be constructed out of a selection of 9 letter tiles in 30 seconds.

No need of sophisticated algorithm to find the "longest word".
With the right dictionary - say 4 to 9 letters, approximately 156,000 scrabble-acceptable words, you can get the best score in less than 1 second. Cost computational time is kn, where n is the dictionary length.
Nine letters beeing given (the given Set), just check for each word of the dictionary (starting by 9 letters) if that word “is included” in the given Set.

BTW,

Wikipedia wrote: It was the first programme to be aired on Channel 4, and 67 series have been broadcast since its debut on 2 November 1982. With over 5,000 episodes, Countdown is one of the longest-running game shows in the world, along with the original French version, Des chiffres et des lettres, which has been running on French television continuously since 1965.

JPF

by **JPF** » Sun Dec 08, 2013 2:08 pm

Hi Leren,

I'm using the same principle as your's, with some twists:

For each group of 4 letters A0A1A2A3, I calculate k = a0 + a1*26 + a2*26^2 + a3*26^3.
where ai = ASC(Ai)-65 ; 0 <= ai < 26
Thus 0 <= k < 456976

Two arrays x(k) and y(k) give the first and the last index of the words starting with A0A1A2A3 in the (sorted) dictionary.
x(k)=0 if there is no such word.

x() and y() may be two-byte data.

I completed the study of 4,5,6,7 word squares. I saved the outputs.
I will summarize and post the results soon.

There are 1,798,889,847 4x4 Word squares! 99% are non-symmetric.

JPF

by **ronk** » Sun Dec 08, 2013 8:31 pm

JPF wrote:With the right dictionary - say 4 to 9 letters, approximately 156,000 scrabble-acceptable words, you can get the best score in less than 1 second. Cost computational time is kn, where n is the dictionary length.
Nine letters beeing given (the given Set), just check for each word of the dictionary (starting by 9 letters) if that word “is included” in the given Set.

Sorry if I missed it earlier in the thread, but what dictionary are you folks using?

by **JPF** » Sun Dec 08, 2013 8:42 pm

ronk wrote:Sorry if I missed it earlier in the thread, but what dictionary are you folks using?

http://thepixiepit.co.uk/scrabble/CSW12.txt

JPF

by **Leren** » Sun Dec 08, 2013 11:10 pm

JPF wrote:
ronk wrote:Sorry if I missed it earlier in the thread, but what dictionary are you folks using?

http://thepixiepit.co.uk/scrabble/CSW12.txt

JPF

I sourced the dictionary through the following site: http://zyzzyva.net/wordlists.shtml I used the British CSW12 file, which appears to be the same as the Collins Scrabble dictionary.

Leren

by **JPF** » Wed Dec 11, 2013 10:07 pm

8x8 puzzle:

Code: Select all: S C R A B B L E . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

JPF

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