open knight's tour of length 179 on chessboard 6x6x6
ABCD
031512812911817621775451711385560175
17952294034170197033221781178534691285661807112059
304146382732215045130836861114972119586764
169166394891204990231635167627101218682576663160131
424792443789241536161261491229312123150145846594
43164168165882516315413871528315815516285
EFGH
14812517275127103126101
761111407974112137102105110141
124139787317495147104173107100
7713613396117142134113106132109
1469711814399144115108
13515398159156114151157116
Author: Alex Chernov
Date (d/m/y): 07/09/2011
Path: OQGAAFEDGA AFEDKABDEF AAFEHALCEE BRAKREKCEB EFHAPMFAQA LEWAQEGAAD ENOAFDAMAM WEOADEFAAM MRGAHLFMDA KEWOPEEHAP CEDGAFAFAC MQGFAHLELA NEQPBOKVTR ZYMQNBPTRA ONEQSQPLNG ZUOUOOQUOL VZSMQLYNLP XORKLSQEU
k=C/mnn = 0.829
6x6x m=
2
3
4
5
6
7
8
9
C
185
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.

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