closed knight's tour of length 612 on chessboard 9x9x9
ABC
0,61223129201521220221724312821166119020121688127214
13021263314172182521321053689120920489949987
2227342053019161121694351071262131362033909316812596107100
135206294032371847131561116654986207921671389510416598193
28411703138173486176573891745560751065314013736210338897294101146
153132391724962191468513417515259741055267192151139142241102145250181
4217150631904530077825873516624324669158141144249366147244
6444301788315413365242716884417150143302365148369182297
156437981298159155721898029970157188149368183245
DEF
219227110237200215108231392220477224236199196261393470259395254
226111114109230117194221478225474235198195252273420481260263268253274256
391610113124229116239232119282475228223238233270197306262281476265258255397
112123208115240121118251164419222287234269310275272313280609264473267400257276
361290387122293178120307283360289286271308305330359572279266401277316
418292177364311180163296288285376309574373312371516319358573278317406314
291176363179162295304185284377386575374383552329550576321318405324315408327
416161380303186247370515375384415381372320607514323546407326557548
160379187248367184549378385414382551554413322545325556553328565
GHI
466335394429333396465509430437423428454508452
467336421480339334521342510431436469422439425522455468453458588451
479338471520341398587332505482433438507424441590427464506457589460
337472345340399343350523432493512435440449426443511456462459450499
346483518571344349402331352517434491448519442586445504463495461498591584
357608513348403354351558529492601596485490447444524494602497592559500
412347404355594409532353564484577570487526561446583598503496593560501540585
599356595410533568547530537578486603489538525528543600597502541604581539
544411534569531536555606579488535527566563542605580567562582
Author: Alex Chernov
Date (d/m/y): 07/09/2011
Path: RAAFAAFAFD EDAKAFAFDC EEBOEKEFAA FACEOANEEB EFGAAABEEE OAADEDEGAA KEEEOAAFAF DECAAKFEEO KBEOLPPDED EGAAFAFACH FEDANAPPED EFAAFAAFAF DEDAKKPMME RNRCLXGAFD GAFAAAFEED CKMRHMWCNW AAABMMQAMN FAAQEZAAFA KFEOBEEMKL AOPPQAFDAM MMRAVEYOLK AKRPQMMEXO EGABEMARKA AFQEBAMRKE NNAOFLZELA PPQAFAFDCE DGAFAFACNA FABQNOEEDD AMGFAADFAM FAAKRANVQL EYOAPBNQEB NOBREBEEDF AFAAFAAFLB YBCEDEFAAF AAFEDEGAAA FAFDEECKDK MKRANARMAO PFCEEBEFKA OEBEEBLKMP QPOOKONQEK EOEEKAFAQE ECNKAMMPPP OOAFAFACMQ EFAFACAFAF AFAFAFDDAO BDEDEGAAFA FDECLKEWKT REKLEOLEZA MZNRAFAFAC DEBRAFAAAF EEDCLOKPME RKNNMPXKOL AONRFDGALF EBEEOKAQOD EEDVKAOKVP FCRKYMAPYE KRKLNYQTEP LMHKEQWEHO AHLPFLLXEK REESEPRDVW LONOEMTPLT LU
k=C/mnn = 0.840
9x9x m=
2
3
4
5
6
7
8
9
C
612
k
.84


Uncrossed closed knight's tours
nxn\m
23456789
2x24444668
3x381828
4x4204256
5x540106
6x6184
7x7292
8x8432
9x9612

Uncrossed open knight's tours
nxn\m
23456789
2x23344778
3x391830
4x4234256
5x540108
6x6185
7x7292
8x8438
9x9621

Last changes
author
date
(d/m/y)
size
path
Alex Chernov27/10/20134x4x4 (56) openBEFKBDFAFK CDGOLYENKC WSDROEKPQA FEKTPYUKYR TYASZNQAMU OXELVG
Alex Chernov27/10/20134x4x4 (56) openBEFKBDFAFK CDGOLYENKC WSDROEKPQA FEKTPYUKYR TYASZNQAMV CXRAVM
Alex Chernov27/10/20134x4x4 (56) openBEFKBDFAFK CDGOLYENKC XNZAMPFAUO FQAMPVWANL YMKNXFKYTM PKGZPE
Alex Chernov27/10/20135x5x5 (108) openDFAFABQEGA BEKFEOBEEO ACDFAFALEW AFDAQFAAFE HBEKDDAKRM MKRMAOPDMK RKFWTPYQUR PTRGKMAYMZ SALEZHQLHP ELKMNXUROE BWEHKLZL
Alex Chernov27/10/20134x4x3 (42) openEGADAQFANQ APGUPQGHCN QTPRSWCKER KPUYTRANQA PV
Alex Chernov27/10/20135x5x2 (40) openAAFEHQACFL ARMAQFLAON EHPMRACDFL OHNQMHQBLO
Alex Chernov27/10/20136x6x6 (184) openAABDEFAAFE KACDEGADKA FDAMEGAADE RADAMRCNGA AFEDOABMER AKFQABLYGN EKPPQELUON AZDKXQEGAA DENALMRWAM NEHAPMMPOE NKEOANLEPE NWOAPEECLW FAAFAFDEGA AFLEEOALES EYVWAAFMAU EOKYWMPELA QAKRNVPEEU XAQPKRNASP LYQU
Alex Chernov27/10/20136x6x6 (178) closedAABDEFAAFE KACDEGADKA FDAMEGAADE RADAMRCNGA AFEDOABMER AKFQABLYGN EKPPQELUON AZDKXQEGAA DENALMRWAM NEHAPMMPOE NKEOANLEPE NWOAPEECLW FAAFAFDEGA AFLEEKWMAA QELAQAKNNY QMSAYANUEO KYWMAVPEEU XARPLQNN
Alex Chernov27/10/20136x6x6 (180) closedAAFEDAAMEG AADEKAFDAM EGAADEKAFD AREEHABEEK ADDAONREKX DAPMEFAFHC HMALQNDBRA NDZFLLXNKH EDGWKPLEPE RGAAFPBMEK NKEDYOALQO EKEQGAAFMA MPAZBEDFAF AFABVEECXT OUSQWNZRKP BENMXNSWPE BLONONQAMN KDOPVRXEDL
Alex Chernov27/10/20136x6x6 (184) closedCDEGADKAFD AMEGAADERA DAMRCNGAAF EDOABMERAK FQABLYGNEK PPQAFDAQEG AADENADAKR EECBKMRSAZ DKMREOAFAM EWAPEEHABE EKAFMDAMAK EWEPLYKNRA NWMQOACBED FAFAFANBLZ LQMRFVWBLK WMQUVZGULP XZNKOELMWR UPOAFNOTQS TRWL
Alex Chernov27/10/20136x6x6 (185) openAACDEGADKA FDAMEGAADE KAFDAREEHA BEEKADDAON REKXDAPMEF AFHCHMALQN DBRANDZFLL XNKHEDGWKP LEPERHACKN XCQEGAADEO AFDANEEHAB EELKNKEDYX NSWAMPQLSR PRAKRFPDCF HHMMWHSWDD NKYMPHLKWN VDOQPHNUYL KYPMNWDLKM YOKVQ
Alex Chernov27/10/20137x7x7 (292) closedAFAFACMEFA AAFEEFAAAF EKBCBEDEGA AFEDGAAFED KAACDEFAAF ALEDFAFAAF AFDEFAAFAB PDKEEOLQEN OEGAAFAMPE BELOEPRAAM MKZENKEXKA QOBNREKLPL QREELLWFKM NAAONFQMAO QQAKFMAQAQ AMAOPMEOOD EDGAFAFACH FEDAKEBEBE BEGFAFAAFA MEMTXWAFAA FMAPMAXMQO EFAAAFEEFA AAFEKBEEDB CNLWOAMREF KKEOQAKTRX LLZEELQBUZ NSPZKRANEQ AASQRKUQMX UZPKMPKLVM WW

new knight tour

Author:

Path:

You can use two forms to enter the tour:

a) Matrix form. Example: the tour

A B C
0,18 8 9 2 13 14 4
6 17 12 5 7
10 1 15 11 3 16

can be defined as string [3,3,3](0,18 . 8)(. 6 17)(10 1 .)(9 2 13)(12 . .)(15 . 11)(14 . 4)(5 . 7)(. 3 16)

The first three numbers is the size of the board. For empty cells indicate the point.

b) Vector form

Each character in path is the direction from the last waypoint:

xyz
xyz
xyz
A2-10K20-1S10-2
B1-20L0-2-1T0-1-2
C-1-20M-20-1U-10-2
D-2-10N02-1V01-2
E-210O201W102
F-120P0-21X0-12
G120Q-201Y-102
H210R021Z012

That the same path in vector notation: GPRBESWTQNODAQNOTD

Links:
Comments
30.01.2012 06:30 Awani Kumar
It is nice that you have discovered longer non-crossing Knight\'s Tours in 3D. I had only shown the possibility of non-crossing knight\'s tour vide the arxiv paper in the year 2008. I had constructed the non-crossing paths by pen and paper.
My recent paper on Magic Tours of Knight in Higher Dimensions has appeared in arxiv.org 1201.0458.html. Please see it and send your comments.
arXiv:1201.0458v1
Regards,
Awani Kumar

01.02.2012 10:28 Alex Chernov
I am amazed that you managed to find a long non-crossing paths using only pen and paper.
Thanks for the link to interesting stuff.


22.05.2019 12:52 Aly Chiman
Hello there, My name is Aly and I would like to know if you would have any interest to have your website here at alex-black.ru promoted as a resource on our blog alychidesign.com ?

We are updating our do-follow broken link resources to include current and up to date resources for our readers. If you may be interested in being included as a resource on our blog, please let me know.

Thanks, Aly

05.12.2019 05:56 Mitchell
I'm from England

05.12.2019 05:56 Garland
I'm interested in this position

05.12.2019 05:56 Brock
Can I take your number?

05.12.2019 05:56 Maurice
Stolen credit card

05.12.2019 05:56 Errol
Will I have to work shifts?

12.02.2020 06:40 Lorenzo
I'd like to pay this in, please

12.02.2020 06:40 Nathanial
How much were you paid in your last job?

12.02.2020 06:40 Albert
Could I have a statement, please?

12.02.2020 06:40 Sherwood
Very interesting tale

12.02.2020 06:40 Demetrius
I sing in a choir
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