closed knight's tour of length 606 on chessboard 9x9x9
ABC
11559321726956512662755438312677323027671232
1310331661195027127453211156274227110777280171
125734156021186930521112354277726810976265290793009170
491459222891162720630,606113361172782616411727526483782998188
58232881152667291263711827926228740245684384510239828714023790
11425662835964482632863924445421493582852402438614136089138173
241192801531226524612516628138509461291524412750885142361248139146167136
15412124712416515013547130155250128159164143362249145158137148499
120132123151134161131156251133160163282144157252147498162
DEF
2702299429123192235604478189302292187533530210477303208293
228952739893234101479190226193188515196233211480319214209294217492
60527297108301100259236103534225192514195296207186529318213224295216475520219
9610729899260105102519170191392199194297197204493212223348215474221218517
177106175238104185200512523198203258521206535371222513522369220495
242391176179350387174169494524349202257398205518255372393399370375380397368
178511388181168385184357506201352401384569256365496527400374503402377568381
284241180363386183356254353390549351364500367550373504419376501564379
507283182355570253497354389548383366571505418502559378547382561
GHI
308603531306597476304593532329595322325438594436596434
481320307310316305516330332321324599437440445598435
336309317312488315342602335328323600326489592439458601442446433
347482311338487314341396491331333426327490424459441456444448
528337536313340395472343404591334427484537425432471457590443454447538450
525346339394473344405412428483486431540423574460455588539452449
408555526345406411546403414551485430541422585470567589462453586465451468
553420407410545416413572565429542421584563580575461554587464581576467573
409544417582577560415543556583558562579552463557466578469566
Author: Alex Chernov
Date (d/m/y): 07/09/2011
Path: AAAFAFACME DFAFAAAFAF DEEFAAAFAB PMEEOEEGAA AFAFDEECLP AFAAMQNFAA AONFEDAOLW CEDEFAAFAA FEDEGAAAFA CPEDEFAAFA AFAFDEDAMA KEENAAQENF AAFAABREDE EKOKAXEBEB EEEHAAFALN EPMEOEOAKE KWMAMAYQAB LNRQDEDGAF AFAABPCEDE FAAFAAFEDE GAAAFACPED EFAAFAAFAF DEDAMAUQAK OKZMAFNQME RCKKANEXEK EOOAPEDALE SEEPALQFLW VZAUAONEEN QRODLKAMAX POOEEKEMKA QPOOEDEDGA FAFAADEMAQ OAFAAFEDCE GBGEBMGAFA AAFEEDCKNK RDEHKAATMY EEOOAFAPDE DEGAAFAFAC HFMCKEBERD LPROAANMQE KOOBEEEDGA AAFAFDEMAQ OAABEDEEGA AAPBEDEDGA FAFACHFAFA FDEBEBEBEG FAFAAFAAFL BMELAPMMEO QGRAFALAOE KLNNXNNMAY QEBEELNLKP RPOLAWNNLX NQMEYHMPLB OQUNROOOEK EEEKAANMDQ XRTWTROKUO KYDSOZLUMN OXWLFQVWKD QVQAAQEBEB MPLOKOUZKE QMLUNV
k=C/mnn = 0.831
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.

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