closed knight's tour of length 288 on chessboard 7x7x7
ABCD
0,288284942142832068790384348468912477282205887596
2851041139439912314052874750554584279767919812974
20712932101544132209429116720849861155295561337822512881114123
119221116382128661303762722085516022154138838013073222
2121763201176633362869642513459216531465712221513214782113260145
6219118141221403526711392695812121927013725013125472
1811914223686521334217701432467135120218259144247214136249112261
EFGH
20422697200125102275154203227152201173274202171192
98199126101170197278281156153159190175172191178
276127100169150103155273158168151174231177228193180
99280149104223196109162157160165256277176229182179189
148105224195108235262271232161164243194167230183272239186181242
268107234251110255246163266237166253267238185252188257
106233248111244263258245240265236184187241264
Author: Alex Chernov
Date (d/m/y): 07/09/2011
Path: RAAFAFACME FAAAFEEFAA AFEOBEBEBE BEFGADAKBQ MAONXDEDGA FAFACHFEDA MNAONBRMPF AWCBDEDGAF AFDCNALWKM ENAAZPQEFA AAFEEFAAAF EKCBMKNEEW AAPLYEEKAF FDCNGODCNK KEOOPMQQAA OCEDFAFAAF EDGAAFACMA XEDFAFAAFA FDEFAAFABL QAFNMABMQA OQMMKUNYKK EERWCKNOAL QOQELPOREE BNNAARDQAN OBMNQDVOKD OYKUOPRVUP GPFWMDQSSQ XOLPMNZLSR PTUKERPT
k=C/mnn = 0.840
7x7x m=
2
3
4
5
6
7
8
9
C
292
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.

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