OFFSET
1,3
COMMENTS
A crippled knight moves one square vertically and two horizontally (or vice versa) and can't land on or pass over any square on which it is previously rested. The initial placement counts as the first move.
a(9) >= 63. - Jud McCranie, May 25 2021
a(9) >= 66. - Giovanni Acerbi, May 20 2024
REFERENCES
A crippled knight is defined by Dario Uri in the Journal of Recreational Mathematics, problem 2465, Vol. 29 #4.
Vol. 30 #4 has an example for 8 X 8 with 48 moves found by Henry Ibstedt.
EXAMPLE
For 3 X 3, the longest path is:
1 . 3
4 . .
. 2 5
The knight cannot move from #5 because it would have to cross over 2 or 3, so a(3)=5.
For 8 X 8, a(8)=51 has a unique solution:
. 1 8 19 22 25 28 31
7 20 23 26 29 32 . .
2 9 18 21 24 27 30 33
. 6 3 10 17 34 37 40
4 11 16 35 38 41 . .
49 46 5 12 15 36 39 42
. . 50 47 44 13 . .
51 48 45 14 . . 43 .
Best known solution for 9 X 9 (66 moves):
. 56 53 50 47 44 27 . .
. . . 55 52 49 46 43 28
57 54 51 48 45 42 29 26 .
64 61 58 41 38 35 32 . 30
. . 65 62 59 40 37 34 25
66 63 60 39 36 33 24 31 .
. 2 5 8 11 14 17 20 23
4 7 10 13 16 19 22 . .
1 . 3 6 9 12 15 18 21
CROSSREFS
KEYWORD
nonn,walk,hard,more
AUTHOR
Jud McCranie, Jun 29 2002
EXTENSIONS
a(8) by Jud McCranie, Mar 18 2021
STATUS
approved