open knight's tour of length 621 on chessboard 9x9x9
ABC
13364131627318850147132481308146261981292418732189
6663691406172257495214158474629928251863114234
651486815160718077134511525954837457124271462013014336338245
671501037079764631002585313675561399845029144372602294235464
14910415315810710278123154135202551381571221191453826122841844491
1591061171091011124511371561211181749762022740852844390311
10511620310811131220815526216120431312016839862853168931016992217
452206115110164113621160453314163318173961654543158831917093218269304
207263205114167264209162317172951662718717194219270216
DEF
2561991792781971282320358128038342771967387236357279234355276
180185194127221946105313843404195636918237362235240405233
2003591822811782311262119025524031053701918275402363588239382232247466
1812262591841932961772301255301136114940617460243238381366241246459368249
1832242822211922971764493601332440716293274465254607242245458251248332
2254562832225252981752682131232538015292295299410529244457252373524409250581
286223526323220267212309619606327544379322291294273448253374523408543378331414
617320287266211308303214411326455321290520305300375616527542377330415517
288265210307302215412272328289519306301413618605376329416569518574
GHI
401536589336591356334467388471468393481590474477
337532385340335586343490389472593469392489395482484473592476491
535386339364587342371354333400537470391488397394493584487480475492585478511
338365346341372367344351582390533398433500561396431534483594485504479512501562
347538608345350421494353399434539596495432439580486505600513502597510583
602609528349422499352419516435540595496611438515430441506601610503598509560563554
348423498545420427575446497612437514443440603599508613564555572579
424541546426521552429418615436444547568559442551507614565556553576
447425522549428417570577604445548567558550573566557571578
Author: Alex Chernov
Date (d/m/y): 07/09/2011
Path: AFAAFAAFED EFAAFAABMA FDAMEDFAFA AAFAFDEEFA AAFABLEDED GAFAFAADEK ADEDFAFAAF AADREKAFDA PRMREEFAAA AFEEKABCBN FDDEFAAFAF AAFEDDAOAF DAKPZDDAMK MQMRGAFAAL QOEEEBLNFA AQNQGAAMER AFAKOEKPQE EKABYADDCE FAFACKASWR QNDCOAMMQF KNNONDEPGW AAAFEKBEEP BEEBEBNAAO DWADEDEGAA FEDGAAAFAF DEECLLVGWK ENNQWAAANE KWPCBPMMWM NGEKEQHEOA ADAGDLHEOG EMAKYEMAAM AVQEQANAQQ OAMPEFAFOA ABPCEDEFAA FAAFEDEGAA AFACLQMMNR APEOEKOKLE WENEEHAAMD PALEWELWEG AAAFAFDEEC LNKAONERAK NEOPEEOACE BEEEHAAFAP BEDEEGAAAF AFDEECNLLT NNOQWLWAAK LUNWZPPQEE BEOAFAAFED CEGBGEBKAK YEKNQEEKAP OEEBEEGAAA BEENAKNEMA YELAUEZPML BWRQTBRNOE NKAMWEOEKO AMWBEEEKAP LOFEEEKAVO YBNSPZVYBL VPZLQTEMPW SZMRNAOEEB EUZNSLPOEW KEOEMSUZLT N
k=C/mnn = 0.852
9x9x m=
2
3
4
5
6
7
8
9
C
621
k
.85


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
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