open knight's tour of length 438 on chessboard 8x8x8
ABC
0971361843910135138152147121269178137
21518411421776381113413914421723121673701337620768
218540141176533131140131916179144721831327518014378199
371884255344350122592018712851182518974181807725467
13032563544553214521186129521752456182812622578479126147
36455431496019053174232649526871732588392127868966
46304861992922263942798571468293428859065266195
1914762965963289758101884291929164265194100
DEF
108213202106200230203151228201149219350229235222227
218110107206113105233152217374155150237158234221238369224
109260205112211198115148204373154275236157208197220239244223276421226
232111210117114104253153274161156209252159166240243376251225246395
261118427272121116331196162271335160165422317347372409242245414315248
273120269330123103435336377164423404167394384241326337250247418323
119270171122267332125318170163426405168319316339327406387334325338249
172268193124321102430169320329340322434328381424333324341
GHI
280351278353349438296352291
281358375370279284289368297302357290420293
348371283304413286277437299412295292354
345282303285306419288298359301356415294367
436407346305314287308393385300361408411364355396
379344313382307416403310360383410363400366417
386389378343312309433362399388365397392
431380425390401342311432398391402
Author: Alex Chernov
Date (d/m/y): 07/09/2011
Path: HEGAAADEDO EFAAAFAFDE EGAAAFEEDK AABEEECPAN AONEEEHAAB QEEKAOFEKB EEQOAACBDE DFAFAAFAFD EFAAFAKFPE EBEKANQAKZ MWBCBDEDFA FAAFAFDEFA AFAFALELEM POAMAKWMEE KAZKNRPPPE DEFAAFAAFE DEGAAAFEED KELKALAXNQ EEBLNRAMYN NWOKAPPMKP QMQFKAKZEM ALQMVWWMXG AAFAFACMQM VRPOANAQEE GADAGAFAFD CKKMUEWELX FKNARAQEBE PKEPAOOCED EGAAFAFACQ AFAFDCEFAF ACNAFAFAFA FDDAKNBNQE KOPFDDEHKL AFZDLEOHKE OQDDCHMPPS OOKRFDCMRF AFAAFABLMQ ENLAYNNZDG KPQUXNKWMH OALVPZFEDA NOLUEQPOUZ ACKNXNOUPP VNERQTLNEW YODVLXPB
k=C/mnn = 0.855
8x8x m=
2
3
4
5
6
7
8
9
C
438
k
.86


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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