A072174 Maximum path length of a crippled knight on an n X n board.
1, 1, 5, 9, 16, 27, 38, 51, 66
Offset: 1
Examples
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
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.
Extensions
a(8) by Jud McCranie, Mar 18 2021
a(9) by Jud McCranie, Aug 12 2025
Comments