(In reply to
computer solution by Charlie)
The following allows verification, step by step, that the solution would actually work:
The initial position:
x x x
RMHUTNPPA
SMEYAPYRC
First we form xxPAPYRUS on the lower row:
D: 4R/2R:
RMHxTxPPx xPPxRMHxT
SMEUANYRA RASMEUANY
Y P C Y P C
U: x M T 2L/1R: x M T
xPPMRUHxY PMRUHxYxP
RASYEPANC CRASYEPAN
D: 3R/4L:
PMRxHMYxT YxTPMRxHM
CRAUYxPAP YxPAPCRAU
S E N S E N
U: P R M 4R/4L: P R M
YxTAMCxHU CxHUYxTAM
YxPSPERAN PERANYxPS
D: 4R/4R:
CxHPYRTAM RTAMCxHPY
PERUNxxPM xxPMPERUN
A Y S A Y S
U: M x Y
RTAMCEHPN
xxPAPYRUS
----------
Then we start the bubble sort, through conjugations (one operation in this mode of description, as 2 leftward moves will be described as just 2L--one operation), alternating with a standard sequence to swap positions 1 and 2:
1L: M x Y
TAMCEHPNR
xxPAPYRUS
----------
so then the first swap:
D: 1R:
TAMMExPNY YTAMMExPN
xxPCPHRUR xxPCPHRUR
A Y S A Y S
U: M E N 1R: M E N
YTACMHxPR RYTACMHxP
xxPAPYRUS xxPAPYRUS
D: 2R:
RYTMCEHxN xNRYTMCEH
xxPAPMRUP xxPAPMRUP
A Y S A Y S
U: Y M H 3L: Y M H
xNRATMCEP ATMCEPxNR
xxPAPYRUS xxPAPYRUS
D: 4L:
ATMYEMxNH EMxNHATMY
xxPCPPRUR xxPCPPRUR
A Y S A Y S
U: N A Y 1L: N A Y
EMxCHPTMR MxCHPTMRE
xxPAPYRUS xxPAPYRUS
D: 1L:
MxCNPAMRY xCNPAMRYM
xxPHPTRUE xxPHPTRUE
A Y S A Y S
U: P M M 2R: P M M
xCNHATRYE YExCNHATR
xxPAPYRUS xxPAPYRUS
D: 3R:
YExPNMATM ATMYExPNM
xxPCPHRUR xxPCPHRUR
A Y S A Y S
U: Y x M
ATMCEHPNR
xxPAPYRUS
----------
The second conjugation:
1L: Y x M
TMCEHPNRA
xxPAPYRUS
----------
The second swap:
D: 1R:
TMCYHxNRM MTMCYHxNR
xxPEPPRUA xxPEPPRUA
A Y S A Y S
U: C H R 1R: C H R
MTMEYPxNA AMTMEYPxN
xxPAPYRUS xxPAPYRUS
D: 2R:
AMTCEHPxR xRAMTCEHP
xxPMPYRUN xxPMPYRUN
A Y S A Y S
U: M C P 3L: M C P
xRAMTYEHN MTYEHNxRA
xxPAPYRUS xxPAPYRUS
D: 4L:
MTYMHCxRP HCxRPMTYM
xxPEPNRUA xxPEPNRUA
A Y S A Y S
U: R M M 1L: R M M
HCxEPNTYA CxEPNTYAH
xxPAPYRUS xxPAPYRUS
D: 1L:
CxERNMYAM xERNMYAMC
xxPPPTRUH xxPPPTRUH
A Y S A Y S
U: N Y C 2R: N Y C
xERPMTAMH MHxERPMTA
xxPAPYRUS xxPAPYRUS
D: 3R:
MHxNRYMTC MTCMHxNRY
xxPEPPRUA xxPEPPRUA
A Y S A Y S
U: M x Y
MTCEHPNRA
xxPAPYRUS
----------
... and the remaining conjugations and swaps:
1L: M x Y
TCEHPNRAM
xxPAPYRUS
----------
D: 1R:
TCEMPxRAY YTCEMPxRA
xxPHPNRUM xxPHPNRUM
A Y S A Y S
U: E P A 1R: E P A
YTCHMNxRM MYTCHMNxR
xxPAPYRUS xxPAPYRUS
D: 2R:
MYTEHPNxA xAMYTEHPN
xxPCPMRUR xxPCPMRUR
A Y S A Y S
U: Y E N 3L: Y E N
xAMCTMHPR CTMHPRxAM
xxPAPYRUS xxPAPYRUS
D: 4L:
CTMYPExAN PExANCTMY
xxPHPRRUM xxPHPRRUM
A Y S A Y S
U: A C Y 1L: A C Y
PExHNRTMM ExHNRTMMP
xxPAPYRUS xxPAPYRUS
D: 1L:
ExHARCMMY xHARCMMYE
xxPNPTRUP xxPNPTRUP
A Y S A Y S
U: R M E 2R: R M E
xHANCTMYP YPxHANCTM
xxPAPYRUS xxPAPYRUS
D: 3R:
YPxRAMCTE CTEYPxRAM
xxPHPNRUM xxPHPNRUM
A Y S A Y S
U: Y x M
CTEHPNRAM
xxPAPYRUS
----------
1L: Y x M
TEHPNRAMC
xxPAPYRUS
----------
D: 1R:
TEHYNxAMM MTEHYNxAM
xxPPPRRUC xxPPPRRUC
A Y S A Y S
U: H N M 1R: H N M
MTEPYRxAC CMTEPYRxA
xxPAPYRUS xxPAPYRUS
D: 2R:
CMTHPNRxM xMCMTHPNR
xxPEPYRUA xxPEPYRUA
A Y S A Y S
U: M H R 3L: M H R
xMCETYPNA ETYPNAxMC
xxPAPYRUS xxPAPYRUS
D: 4L:
ETYMNHxMR NHxMRETYM
xxPPPARUC xxPPPARUC
A Y S A Y S
U: M E M 1L: M E M
NHxPRATYC HxPRATYCN
xxPAPYRUS xxPAPYRUS
D: 1L:
HxPMAEYCM xPMAEYCMH
xxPRPTRUN xxPRPTRUN
A Y S A Y S
U: A Y H 2R: A Y H
xPMRETCMN MNxPMRETC
xxPAPYRUS xxPAPYRUS
D: 3R:
MNxAMYETH ETHMNxAMY
xxPPPRRUC xxPPPRRUC
A Y S A Y S
U: M x Y
ETHPNRAMC
xxPAPYRUS
----------
1L: M x Y
THPNRAMCE
xxPAPYRUS
----------
D: 1R:
THPMRxMCY YTHPMRxMC
xxPNPARUE xxPNPARUE
A Y S A Y S
U: P R C 1R: P R C
YTHNMAxME EYTHNMAxM
xxPAPYRUS xxPAPYRUS
D: 2R:
EYTPNRAxC xCEYTPNRA
xxPHPMRUM xxPHPMRUM
A Y S A Y S
U: Y P A 3L: Y P A
xCEHTMNRM HTMNRMxCE
xxPAPYRUS xxPAPYRUS
D: 4L:
HTMYRPxCA RPxCAHTMY
xxPNPMRUE xxPNPMRUE
A Y S A Y S
U: C H Y 1L: C H Y
RPxNAMTME PxNAMTMER
xxPAPYRUS xxPAPYRUS
D: 1L:
PxNCMHMEY xNCMHMEYP
xxPAPTRUR xxPAPTRUR
A Y S A Y S
U: M M P 2R: M M P
xNCAHTEYR YRxNCAHTE
xxPAPYRUS xxPAPYRUS
D: 3R:
YRxMCMHTP HTPYRxMCM
xxPNPARUE xxPNPARUE
A Y S A Y S
U: Y x M
HTPNRAMCE
xxPAPYRUS
----------
1L: Y x M
TPNRAMCEH
xxPAPYRUS
----------
D: 1R:
TPNYAxCEM MTPNYAxCE
xxPRPMRUH xxPRPMRUH
A Y S A Y S
U: N A E 1R: N A E
MTPRYMxCH HMTPRYMxC
xxPAPYRUS xxPAPYRUS
D: 2R:
HMTNRAMxE xEHMTNRAM
xxPPPYRUC xxPPPYRUC
A Y S A Y S
U: M N M 3L: M N M
xEHPTYRAC PTYRACxEH
xxPAPYRUS xxPAPYRUS
D: 4L:
PTYMANxEM ANxEMPTYM
xxPRPCRUH xxPRPCRUH
A Y S A Y S
U: E P M 1L: E P M
ANxRMCTYH NxRMCTYHA
xxPAPYRUS xxPAPYRUS
D: 1L:
NxRECPYHM xRECPYHMN
xxPMPTRUA xxPMPTRUA
A Y S A Y S
U: C Y N 2R: C Y N
xREMPTHMA MAxREMPTH
xxPAPYRUS xxPAPYRUS
D: 3R:
MAxCEYPTN PTNMAxCEY
xxPRPMRUH xxPRPMRUH
A Y S A Y S
U: M x Y
PTNRAMCEH
xxPAPYRUS
----------
1L: M x Y
TNRAMCEHP
xxPAPYRUS
----------
D: 1R:
TNRMMxEHY YTNRMMxEH
xxPAPCRUP xxPAPCRUP
A Y S A Y S
U: R M H 1R: R M H
YTNAMCxEP PYTNAMCxE
xxPAPYRUS xxPAPYRUS
D: 2R:
PYTRAMCxH xHPYTRAMC
xxPNPMRUE xxPNPMRUE
A Y S A Y S
U: Y R C 3L: Y R C
xHPNTMAME NTMAMExHP
xxPAPYRUS xxPAPYRUS
D: 4L:
NTMYMRxHC MRxHCNTMY
xxPAPERUP xxPAPERUP
A Y S A Y S
U: H N Y 1L: H N Y
MRxACETMP RxACETMPM
xxPAPYRUS xxPAPYRUS
D: 1L:
RxAHENMPY xAHENMPYR
xxPCPTRUM xxPCPTRUM
A Y S A Y S
U: E M R 2R: E M R
xAHCNTPYM YMxAHCNTP
xxPAPYRUS xxPAPYRUS
D: 3R:
YMxEHMNTR NTRYMxEHM
xxPAPCRUP xxPAPCRUP
A Y S A Y S
U: Y x M
NTRAMCEHP
xxPAPYRUS
----------
2L: Y x M
RAMCEHPNT
xxPAPYRUS
----------
D: 1R:
RAMYExPNM MRAMYExPN
xxPCPHRUT xxPCPHRUT
A Y S A Y S
U: M E N 1R: M E N
MRACYHxPT TMRACYHxP
xxPAPYRUS xxPAPYRUS
D: 2R:
TMRMCEHxN xNTMRMCEH
xxPAPYRUP xxPAPYRUP
A Y S A Y S
U: M M H 3L: M M H
xNTARYCEP ARYCEPxNT
xxPAPYRUS xxPAPYRUS
D: 4L:
ARYMEMxNH EMxNHARYM
xxPCPPRUT xxPCPPRUT
A Y S A Y S
U: N A M 1L: N A M
EMxCHPRYT MxCHPRYTE
xxPAPYRUS xxPAPYRUS
D: 1L:
MxCNPAYTM xCNPAYTMM
xxPHPRRUE xxPHPRRUE
A Y S A Y S
U: P Y M 2R: P Y M
xCNHARTME MExCNHART
xxPAPYRUS xxPAPYRUS
D: 3R:
MExPNYARM ARMMExPNY
xxPCPHRUT xxPCPHRUT
A Y S A Y S
U: M x Y
ARMCEHPNT
xxPAPYRUS
----------
2L: M x Y
MCEHPNTAR
xxPAPYRUS
----------
D: 1R:
MCEMPxTAY YMCEMPxTA
xxPHPNRUR xxPHPNRUR
A Y S A Y S
U: E P A 1R: E P A
YMCHMNxTR RYMCHMNxT
xxPAPYRUS xxPAPYRUS
D: 2R:
RYMEHPNxA xARYMEHPN
xxPCPMRUT xxPCPMRUT
A Y S A Y S
U: Y E N 3L: Y E N
xARCMMHPT CMMHPTxAR
xxPAPYRUS xxPAPYRUS
D: 4L:
CMMYPExAN PExANCMMY
xxPHPTRUR xxPHPTRUR
A Y S A Y S
U: A C Y 1L: A C Y
PExHNTMMR ExHNTMMRP
xxPAPYRUS xxPAPYRUS
D: 1L:
ExHATCMRY xHATCMRYE
xxPNPMRUP xxPNPMRUP
A Y S A Y S
U: T M E 2R: T M E
xHANCMRYP YPxHANCMR
xxPAPYRUS xxPAPYRUS
D: 3R:
YPxTAMCME CMEYPxTAM
xxPHPNRUR xxPHPNRUR
A Y S A Y S
U: Y x M
CMEHPNTAR
xxPAPYRUS
----------
2L: Y x M
EHPNTARCM
xxPAPYRUS
----------
D: 1R:
EHPYTxRCM MEHPYTxRC
xxPNPARUM xxPNPARUM
A Y S A Y S
U: P T C 1R: P T C
MEHNYAxRM MMEHNYAxR
xxPAPYRUS xxPAPYRUS
D: 2R:
MMEPNTAxC xCMMEPNTA
xxPHPYRUR xxPHPYRUR
A Y S A Y S
U: M P A 3L: M P A
xCMHEYNTR HEYNTRxCM
xxPAPYRUS xxPAPYRUS
D: 4L:
HEYMTPxCA TPxCAHEYM
xxPNPRRUM xxPNPRRUM
A Y S A Y S
U: C H M 1L: C H M
TPxNAREYM PxNAREYMT
xxPAPYRUS xxPAPYRUS
D: 1L:
PxNCRHYMM xNCRHYMMP
xxPAPERUT xxPAPERUT
A Y S A Y S
U: R Y P 2R: R Y P
xNCAHEMMT MTxNCAHEM
xxPAPYRUS xxPAPYRUS
D: 3R:
MTxRCYHEP HEPMTxRCY
xxPNPARUM xxPNPARUM
A Y S A Y S
U: M x Y
HEPNTARCM
xxPAPYRUS
----------
1L: M x Y
EPNTARCMH
xxPAPYRUS
----------
D: 1R:
EPNMAxCMY YEPNMAxCM
xxPTPRRUH xxPTPRRUH
A Y S A Y S
U: N A M 1R: N A M
YEPTMRxCH HYEPTMRxC
xxPAPYRUS xxPAPYRUS
D: 2R:
HYENTARxM xMHYENTAR
xxPPPMRUC xxPPPMRUC
A Y S A Y S
U: Y N R 3L: Y N R
xMHPEMTAC PEMTACxMH
xxPAPYRUS xxPAPYRUS
D: 4L:
PEMYANxMR ANxMRPEMY
xxPTPCRUH xxPTPCRUH
A Y S A Y S
U: M P Y 1L: M P Y
ANxTRCEMH NxTRCEMHA
xxPAPYRUS xxPAPYRUS
D: 1L:
NxTMCPMHY xTMCPMHYN
xxPRPERUA xxPRPERUA
A Y S A Y S
U: C M N 2R: C M N
xTMRPEHYA YAxTMRPEH
xxPAPYRUS xxPAPYRUS
D: 3R:
YAxCMMPEN PENYAxCMM
xxPTPRRUH xxPTPRRUH
A Y S A Y S
U: Y x M
PENTARCMH
xxPAPYRUS
----------
2R: Y x M
MHPENTARC
xxPAPYRUS
----------
D: 1R:
MHPYNxARM MMHPYNxAR
xxPEPTRUC xxPEPTRUC
A Y S A Y S
U: P N R 1R: P N R
MMHEYTxAC CMMHEYTxA
xxPAPYRUS xxPAPYRUS
D: 2R:
CMMPENTxR xRCMMPENT
xxPHPYRUA xxPHPYRUA
A Y S A Y S
U: M P T 3L: M P T
xRCHMYENA HMYENAxRC
xxPAPYRUS xxPAPYRUS
D: 4L:
HMYMNPxRT NPxRTHMYM
xxPEPARUC xxPEPARUC
A Y S A Y S
U: R H M 1L: R H M
NPxETAMYC PxETAMYCN
xxPAPYRUS xxPAPYRUS
D: 1L:
PxERAHYCM xERAHYCMP
xxPTPMRUN xxPTPMRUN
A Y S A Y S
U: A Y P 2R: A Y P
xERTHMCMN MNxERTHMC
xxPAPYRUS xxPAPYRUS
D: 3R:
MNxARYHMP HMPMNxARY
xxPEPTRUC xxPEPTRUC
A Y S A Y S
U: M x Y
HMPENTARC
xxPAPYRUS
----------
1L: M x Y
MPENTARCH
xxPAPYRUS
----------
D: 1R:
MPEMTxRCY YMPEMTxRC
xxPNPARUH xxPNPARUH
A Y S A Y S
U: E T C 1R: E T C
YMPNMAxRH HYMPNMAxR
xxPAPYRUS xxPAPYRUS
D: 2R:
HYMENTAxC xCHYMENTA
xxPPPMRUR xxPPPMRUR
A Y S A Y S
U: Y E A 3L: Y E A
xCHPMMNTR PMMNTRxCH
xxPAPYRUS xxPAPYRUS
D: 4L:
PMMYTExCA TExCAPMMY
xxPNPRRUH xxPNPRRUH
A Y S A Y S
U: C P Y 1L: C P Y
TExNARMMH ExNARMMHT
xxPAPYRUS xxPAPYRUS
D: 1L:
ExNCRPMHY xNCRPMHYE
xxPAPMRUT xxPAPMRUT
A Y S A Y S
U: R M E 2R: R M E
xNCAPMHYT YTxNCAPMH
xxPAPYRUS xxPAPYRUS
D: 3R:
YTxRCMPME PMEYTxRCM
xxPNPARUH xxPNPARUH
A Y S A Y S
U: Y x M
PMENTARCH
xxPAPYRUS
----------
1R: Y x M
HPMENTARC
xxPAPYRUS
----------
D: 1R:
HPMYNxARM MHPMYNxAR
xxPEPTRUC xxPEPTRUC
A Y S A Y S
U: M N R 1R: M N R
MHPEYTxAC CMHPEYTxA
xxPAPYRUS xxPAPYRUS
D: 2R:
CMHMENTxR xRCMHMENT
xxPPPYRUA xxPPPYRUA
A Y S A Y S
U: M M T 3L: M M T
xRCPHYENA PHYENAxRC
xxPAPYRUS xxPAPYRUS
D: 4L:
PHYMNMxRT NMxRTPHYM
xxPEPARUC xxPEPARUC
A Y S A Y S
U: R P M 1L: &nbs
|
Posted by Charlie
on 2009-01-15 14:09:35 |