The following is a simple set-up for the familiar Knight's Tour puzzle, in this case on a 5x5 chess board only, with the start/finish positions as indicated:

		1
25

One day, being rather jealous of all the attention the Knight gets with these kind of tours, the Knave loudly proclaimed that he too could complete this same tour board. But of course, as with Liars and Knights puzzles, the Knave will alternate between Knightly moves (the standard chess move) and Liar's moves (2 squares up, down, left, or right, starting and ending on the same color).

Could the Knave complete the tour where he initially starts with a Knightly move? How about starting with a Liar's move? (There may be more than one solution.)

If we label the 25 squares:

a b c d e
f g h i j
k l m n o
p q r s t
u v w x y

the 104 possible routes beginning with a liar's move are:

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mkbdgqfpwynlacjheoxvsitru
mkbdgqfpwynlacjtisvxoehru
mkbdgqfpwynxoehjcalvsitru
mkbdgqfheoxvsitjcalnywpru
mkbdgitjcalvsqfpwynxoehru
mkbdgitjcalvsqfheoxnywpru
mkbdgitjcalnywpfqsvxoehru
mkbdgitjcahrywpfqsvxoenlu
mkvlacfpgqxnywtjsibdoehru
mkvlacfpgibdoehjsqxnywtru
mkvlacfheodbisjtwynxqgpru
mkvxqgpfcalbisjheodnywtru
mkvxqgpfcalbisjtwyndoehru
mkvxqgpfcalnywtjsibdoehru
mkvxqgpfcahrywtjsibdoenlu
mkvxqsjheodbigpfcalnywtru
mkvxqsjtwyrhacfpgibdoenlu
mkvxqsjtwynlacfpgibdoehru
mkvxqsjtwynlacfheodbigpru
mkvxqsjtwyndoehfcalbigpru
mcfpgqxvkalbisjheodnywtru
mcfpgqxvkalbisjtwyndoehru
mcfpgqxvkalnywtjsibdoehru
mcfpgqxvkahrywtjsibdoenlu
mcfpgqxneodbisjtwyrhakvlu
mcfpgiblakvxqsjheodnywtru
mcfpgiblakvxqsjtwyndoehru
mcfpgibdoehjsqxvkalnywtru
mcfpgibdoenxqsjtwyrhakvlu
mcfhakvxqgprywtjsibdoenlu
mcfhakvxqsjtwyrpgibdoenlu
mcfheodbisjtwynlakvxqgpru
mcfheodnywtjsqxvkalbigpru
mcfheodnywtjsiblakvxqgpru
mcjhakbdgqfpwyrtisvxoenlu
mcjhakbdgitrywpfqsvxoenlu
mcjheoxvsqfpwynlakbdgitru
mcjheoxnywpfqgdbkalvsitru
mcjheoxnywpfqsvlakbdgitru
mcjtigdbkalvsqfpwynxoehru
mcjtigdbkalvsqfheoxnywpru
mcjtigdbkalnywpfqsvxoehru
mcjtigdbkahrywpfqsvxoenlu
mcjtigdneoxvsqfpwyrhakblu
mcjtisvlakbdgqfpwynxoehru
mcjtisvlakbdgqfheoxnywpru
mcjtisvxoehfqgdbkalnywpru
mcjtisvxoendgqfpwyrhakblu
mwpfqgdbkalnyoxvsitjcehru
mwpfqgdbkahryoxvsitjcenlu
mwpfqgdbkahryoxnecjtisvlu
mwpfqgdbkahjcenxoyrtisvlu
mwpfqgdnecjtisvxoyrhakblu
mwpfqsvxoyrhakbdgitjcenlu
mwpfqsvxoyrtigdbkahjcenlu
mwpfqsvxoyrtigdnecjhakblu
mwpfqsvxoynlakbdgitjcehru
mwpryoxvsqfhakbdgitjcenlu
mwpryoxvsitjcendgqfhakblu
mwpryoxnecjtigdbkahfqsvlu
mwtryodbigpfcenxqsjhakvlu
mwtryodbisjhakvxqgpfcenlu
mwtryodnecfpgqxvkahjsiblu
mwtjsqxvkalnyodbigpfcehru
mwtjsqxvkahfcendoyrpgiblu
mwtjsqxvkahryodbigpfcenlu
mwtjsqxvkahryodnecfpgiblu
mwtjsqxnecfpgibdoyrhakvlu
mwtjsibdoyrpgqxvkahfcenlu
mwtjsibdoyrpgqxnecfhakvlu
mwtjsibdoyrhakvxqgpfcenlu
mwtjsibdoynlakvxqgpfcehru
modbigpfcehjsqxvkalnywtru
modbigpfcenxqsjtwyrhakvlu
modbigprywtjsqxvkahfcenlu
modbigprywtjsqxnecfhakvlu
modbisjhecfpgqxvkalnywtru
modbisjtwyrpgqxvkahfcenlu
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modbisjtwyrhakvxqgpfcenlu
modbisjtwynlakvxqgpfcehru
modnecfpgqxvkahrywtjsiblu
modnecfhakvxqgprywtjsiblu
modnecfhakvxqsjtwyrpgiblu
modnywtjsqxvkalbigpfcehru
modnywtjsiblakvxqgpfcehru
moxvsqfpwyrhakbdgitjcenlu
moxvsqfpwyrtigdbkahjcenlu
moxvsqfpwyrtigdnecjhakblu
moxvsqfpwynlakbdgitjcehru
moxvsqfhecjtigdbkalnywpru
moxvsitrywpfqgdbkahjcenlu
moxvsitrywpfqgdnecjhakblu
moxvsitjcehfqgdbkalnywpru
moxvsitjcendgqfpwyrhakblu
moxnecjhakbdgqfpwyrtisvlu
moxnecjhakbdgitrywpfqsvlu
moxnecjtigdbkahrywpfqsvlu
moxnywpfqgdbkalvsitjcehru
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Posted by Charlie on 2009-01-23 21:39:47