Copyright (c) James A. Storer

Century
(One additional 1/2 unit move at the start precedes this solution.)

######################################################################
Rectilinear steps: 99
Straight-Line steps: 111
Unit steps: 135 (but possible in 131 unit steps)
######################################################################

#0:
1 X X 2
A X X C
A B   C
3 B   4
J J K K

#1. Move 4 on a path of 2 segments ending north:
1 X X 2
A X X C
A B 4 C
3 B    
J J K K

#2. Move K north:
1 X X 2
A X X C
A B 4 C
3 B K K
J J    

#3. Move J east 2 units:
1 X X 2
A X X C
A B 4 C
3 B K K
    J J

#4. Move 3 on a path of 2 segments ending east:
1 X X 2
A X X C
A B 4 C
  B K K
  3 J J

#5. Move A south 2 units:
1 X X 2
  X X C
  B 4 C
A B K K
A 3 J J

#6. Move 1 south 2 units:
  X X 2
  X X C
1 B 4 C
A B K K
A 3 J J

#7. Move X west:
X X   2
X X   C
1 B 4 C
A B K K
A 3 J J

#8. Move 2 west:
X X 2  
X X   C
1 B 4 C
A B K K
A 3 J J

#9. Move C north:
X X 2 C
X X   C
1 B 4  
A B K K
A 3 J J

#10. Move 4 east:
X X 2 C
X X   C
1 B   4
A B K K
A 3 J J

#11. Move 2 south 2 units:
X X   C
X X   C
1 B 2 4
A B K K
A 3 J J

#12. Move X east:
  X X C
  X X C
1 B 2 4
A B K K
A 3 J J

#13. Move 1 north 2 units:
1 X X C
  X X C
  B 2 4
A B K K
A 3 J J

#14. Move A north 2 units:
1 X X C
A X X C
A B 2 4
  B K K
  3 J J

#15. Move 3 on a path of 2 segments ending north:
1 X X C
A X X C
A B 2 4
3 B K K
    J J

#16. Move J west 2 units:
1 X X C
A X X C
A B 2 4
3 B K K
J J    

#17. Move K south:
1 X X C
A X X C
A B 2 4
3 B    
J J K K

#18. Move 4 on a path of 2 segments ending west:
1 X X C
A X X C
A B 2  
3 B 4  
J J K K

#19. Move C south 2 units:
1 X X  
A X X  
A B 2 C
3 B 4 C
J J K K

#20. Move X east:
1   X X
A   X X
A B 2 C
3 B 4 C
J J K K

#21. Move B north 2 units:
1 B X X
A B X X
A   2 C
3   4 C
J J K K

#22. Move 3 on a path of 2 segments ending north:
1 B X X
A B X X
A 3 2 C
    4 C
J J K K

#23. Move J north:
1 B X X
A B X X
A 3 2 C
J J 4 C
    K K

#24. Move K west 2 units:
1 B X X
A B X X
A 3 2 C
J J 4 C
K K    

#25. Move 4 on a path of 2 segments ending east:
1 B X X
A B X X
A 3 2 C
J J   C
K K   4

#26. Move J east:
1 B X X
A B X X
A 3 2 C
  J J C
K K   4

#27. Move K east:
1 B X X
A B X X
A 3 2 C
  J J C
  K K 4

#28. Move A south 2 units:
1 B X X
  B X X
  3 2 C
A J J C
A K K 4

#29. Move 1 south 2 units:
  B X X
  B X X
1 3 2 C
A J J C
A K K 4

#30. Move B west:
B   X X
B   X X
1 3 2 C
A J J C
A K K 4

#31. Move 3 north 2 units:
B 3 X X
B   X X
1   2 C
A J J C
A K K 4

#32. Move 1 east:
B 3 X X
B   X X
  1 2 C
A J J C
A K K 4

#33. Move B south:
  3 X X
B   X X
B 1 2 C
A J J C
A K K 4

#34. Move 3 west:
3   X X
B   X X
B 1 2 C
A J J C
A K K 4

#35. Move X west:
3 X X  
B X X  
B 1 2 C
A J J C
A K K 4

#36. Move C north 2 units:
3 X X C
B X X C
B 1 2  
A J J  
A K K 4

#37. Move J east:
3 X X C
B X X C
B 1 2  
A   J J
A K K 4

#38. Move 1 south:
3 X X C
B X X C
B   2  
A 1 J J
A K K 4

#39. Move 2 west:
3 X X C
B X X C
B 2    
A 1 J J
A K K 4

#40. Move J north:
3 X X C
B X X C
B 2 J J
A 1    
A K K 4

#41. Move 1 east:
3 X X C
B X X C
B 2 J J
A   1  
A K K 4

#42. Move 4 north:
3 X X C
B X X C
B 2 J J
A   1 4
A K K  

#43. Move K east:
3 X X C
B X X C
B 2 J J
A   1 4
A   K K

#44. Move A east:
3 X X C
B X X C
B 2 J J
  A 1 4
  A K K

#45. Move B south 2 units:
3 X X C
  X X C
  2 J J
B A 1 4
B A K K

#46. Move 2 on a path of 2 segments ending north:
3 X X C
2 X X C
    J J
B A 1 4
B A K K

#47. Move J west 2 units:
3 X X C
2 X X C
J J    
B A 1 4
B A K K

#48. Move 4 on a path of 2 segments ending west:
3 X X C
2 X X C
J J 4  
B A 1  
B A K K

#49. Move C south 2 units:
3 X X  
2 X X  
J J 4 C
B A 1 C
B A K K

#50. Move X east:
3   X X
2   X X
J J 4 C
B A 1 C
B A K K

#51. Move 2 on a path of 2 segments ending north:
3 2 X X
    X X
J J 4 C
B A 1 C
B A K K

#52. Move J north:
3 2 X X
J J X X
    4 C
B A 1 C
B A K K

#53. Move A north:
3 2 X X
J J X X
  A 4 C
B A 1 C
B   K K

#54. Move B north:
3 2 X X
J J X X
B A 4 C
B A 1 C
    K K

#55. Move K west 2 units:
3 2 X X
J J X X
B A 4 C
B A 1 C
K K    

#56. Move 1 south:
3 2 X X
J J X X
B A 4 C
B A   C
K K 1  

#57. Move 4 south:
3 2 X X
J J X X
B A   C
B A 4 C
K K 1  

#58. Move C south:
3 2 X X
J J X X
B A    
B A 4 C
K K 1 C

#59. Move X south:
3 2    
J J X X
B A X X
B A 4 C
K K 1 C

#60. Move 2 east 2 units:
3     2
J J X X
B A X X
B A 4 C
K K 1 C

#61. Move 3 east 2 units:
    3 2
J J X X
B A X X
B A 4 C
K K 1 C

#62. Move J north:
J J 3 2
    X X
B A X X
B A 4 C
K K 1 C

#63. Move A north:
J J 3 2
  A X X
B A X X
B   4 C
K K 1 C

#64. Move 4 west:
J J 3 2
  A X X
B A X X
B 4   C
K K 1 C

#65. Move 1 north:
J J 3 2
  A X X
B A X X
B 4 1 C
K K   C

#66. Move K east:
J J 3 2
  A X X
B A X X
B 4 1 C
  K K C

#67. Move B south:
J J 3 2
  A X X
  A X X
B 4 1 C
B K K C

#68. Move A west:
J J 3 2
A   X X
A   X X
B 4 1 C
B K K C

#69. Move X west:
J J 3 2
A X X  
A X X  
B 4 1 C
B K K C

#70. Move 2 south:
J J 3  
A X X 2
A X X  
B 4 1 C
B K K C

#71. Move 3 east:
J J   3
A X X 2
A X X  
B 4 1 C
B K K C

#72. Move C north:
J J   3
A X X 2
A X X C
B 4 1 C
B K K  

#73. Move J east:
  J J 3
A X X 2
A X X C
B 4 1 C
B K K  

#74. Move A north:
A J J 3
A X X 2
  X X C
B 4 1 C
B K K  

#75. Move B north:
A J J 3
A X X 2
B X X C
B 4 1 C
  K K  

#76. Move K east:
A J J 3
A X X 2
B X X C
B 4 1 C
    K K

#77. Move 4 on a path of 2 segments ending west:
A J J 3
A X X 2
B X X C
B   1 C
4   K K

#78. Move 1 on a path of 2 segments ending south:
A J J 3
A X X 2
B X X C
B     C
4 1 K K

#79. Move X south:
A J J 3
A     2
B X X C
B X X C
4 1 K K

#80. Move 2 west:
A J J 3
A   2  
B X X C
B X X C
4 1 K K

#81. Move 3 south:
A J J  
A   2 3
B X X C
B X X C
4 1 K K

#82. Move J east:
A   J J
A   2 3
B X X C
B X X C
4 1 K K

#83. Move A east:
  A J J
  A 2 3
B X X C
B X X C
4 1 K K

#84. Move B north 2 units:
B A J J
B A 2 3
  X X C
  X X C
4 1 K K

#85. Move X west:
B A J J
B A 2 3
X X   C
X X   C
4 1 K K

#86. Move 2 south:
B A J J
B A   3
X X 2 C
X X   C
4 1 K K

#87. Move 3 west:
B A J J
B A 3  
X X 2 C
X X   C
4 1 K K

#88. Move C north:
B A J J
B A 3 C
X X 2 C
X X    
4 1 K K

#89. Move K north:
B A J J
B A 3 C
X X 2 C
X X K K
4 1    

#90. Move 1 east 2 units:
B A J J
B A 3 C
X X 2 C
X X K K
4     1

#91. Move 4 east 2 units:
B A J J
B A 3 C
X X 2 C
X X K K
    4 1

#92. Move X south:
B A J J
B A 3 C
    2 C
X X K K
X X 4 1

#93. Move 2 west 2 units:
B A J J
B A 3 C
2     C
X X K K
X X 4 1

#94. Move A south:
B   J J
B A 3 C
2 A   C
X X K K
X X 4 1

#95. Move J west:
B J J  
B A 3 C
2 A   C
X X K K
X X 4 1

#96. Move C north:
B J J C
B A 3 C
2 A    
X X K K
X X 4 1

#97. Move K north:
B J J C
B A 3 C
2 A K K
X X    
X X 4 1

#98. Move 4 on a path of 2 segments ending east:
B J J C
B A 3 C
2 A K K
X X   4
X X   1

#99. Move X east:
B J J C
B A 3 C
2 A K K
  X X 4
  X X 1

*** The corresponding straight-line solution may be obtained by:
    Replace step 1 by 2 straight-line steps.
    Replace step 4 by 2 straight-line steps.
    Replace step 15 by 2 straight-line steps.
    Replace step 18 by 2 straight-line steps.
    Replace step 22 by 2 straight-line steps.
    Replace step 25 by 2 straight-line steps.
    Replace step 46 by 2 straight-line steps.
    Replace step 48 by 2 straight-line steps.
    Replace step 51 by 2 straight-line steps.
    Replace step 77 by 2 straight-line steps.
    Replace step 78 by 2 straight-line steps.
    Replace step 98 by 2 straight-line steps.