Copyright (c) James A. Storer
Stacking Cups Problem 1
Generalized rectilinear movement is computed.
One move is pushing a single piece with one finger,
where that piece may push or drag other pieces with it.
A second finger may NOT be used to aid movement,
prevent a piece from being dragged to far, etc.
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Generalized Rectilinear Steps: 31
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#0:
3 3 3 3 3 3 3
3 A A 3
2 2 2 2 2 3 B A A B 3
2 1 1 1 2 B A A A B
C 2 1 1 2 C B B B B B
C 1 1 C
C C C C C C C
#1. Move 2:
2 2 2 2 2 3 3 3 3 3 3 3
2 2 3 A A 3
2 2 3 B A A B 3
1 1 1 B A A A B
C 1 1 C B B B B B
C 1 1 C
C C C C C C C
#2. Move 3:
2 2 2 2 2 3 3 3 3 3 3 3
2 2 3 3
2 2 3 3
1 1 1 A A
C 1 1 C B A A B
C 1 1 C B A A A B
C C C C C C C B B B B B
#3. Move 1:
2 2 2 2 2 3 3 3 3 3 3 3
2 2 3 1 1 1 3
2 2 3 1 1 3
1 1 A A
C C B A A B
C C B A A A B
C C C C C C C B B B B B
#4. Move C:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 1 1 1 3
2 C 2 3 C 1 1 3
C C C C C C C 1 1 A A
B A A B
B A A A B
B B B B B
#5. Move 3:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 1 1 1 3
2 C 2 3 C 1 1 3
C C C C C C C 1 1 A A
B A A B
B A A A B
B B B B B
#6. Move A:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 1 1 1 A 3 A
2 C 2 3 C 1 1 A 3 A
C C C C C C C 1 1 A A A
B B
B B
B B B B B
#7. Move B:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 1 1 1 A 3 A
2 C 2 3 C 1 1 A 3 A
C C C C C C C 1 1 A A A
B B
B B
B B B B B
#8. Move A:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 1 1 1 3
2 C 2 3 C 1 1 3
C C C C C C C 1 1
B B A A
B B A A
B B B B B A A A
#9. Move 2:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 1 1 1 3
2 C 2 3 C 1 1 3
C C C C C C C 1 1
B B A A
B B A A
B B B B B A A A
#10. Move 1:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 3
2 C 2 3 C 3
C C C C C C C
B B A A 1 1 1
B B A A 1 1
B B B B B A A A 1 1
#11. Move C:
2 2 2 2 2 3 3 3 3 3 3 3
2 C 2 3 C 3
2 C 2 3 C 3
C C C C C C C
B B A A 1 1 1
B B A A 1 1
B B B B B A A A 1 1
#12. Move B:
2 2 2 2 2 3 3 3 3 3 3 3
B 2 B C 2 3 C 3
B 2 B C 2 3 C 3
B B B B B C C C C C C C
A A 1 1 1
A A 1 1
A A A 1 1
#13. Move A:
2 2 2 2 2 3 3 3 3 3 3 3
B 2 B C 2 3 C 3
B 2 B C 2 3 C 3
B B B B B C C C C C C C
A A 1 1 1
A A 1 1
A A A 1 1
#14. Move C:
2 2 2 2 2 3 3 3 3 3 3 3
B 2 B 2 3 3
B 2 B 2 3 3
B B B B B
A A C C 1 1 1
A A C C 1 1
A A A C C C C C C C 1 1
#15. Move 1:
2 2 2 2 2 3 3 3 3 3 3 3
B 2 B 2 3 1 1 1 3
B 2 B 2 3 1 1 3
B B B B B 1 1
A A C C
A A C C
A A A C C C C C C C
#16. Move A:
2 2 2 2 2 3 3 3 3 3 3 3
B 2 B 2 3 1 1 1 3
B 2 B 2 3 1 1 3
B B B B B 1 1
A A C C
A A C C
A A A C C C C C C C
#17. Move 2:
2 3 3 3 3 3 3 3
2 3 1 1 1 3
2 3 1 1 3
2 2 2 2 2 1 1
B 2 B A 2 A C C
B 2 B A 2 A C C
B B B B B A A A C C C C C C C
#18. Move A:
2 2 2 2 2 3 3 3 3 3 3 3
2 A 2 A 3 1 1 1 3
2 A 2 A 3 1 1 3
A A A 1 1
B B C C
B B C C
B B B B B C C C C C C C
#19. Move B:
2 2 2 2 2 3 3 3 3 3 3 3
2 A 2 A 3 1 1 1 3
2 A 2 A 3 1 1 3
A A A 1 1
B B C C
B B C C
B B B B B C C C C C C C
#20. Move A:
2 2 2 2 2 3 3 3 3 3 3 3
2 2 3 1 1 1 3
2 2 3 1 1 3
A A 1 1
B A A B C C
B A A A B C C
B B B B B C C C C C C C
#21. Move 2:
2 2 2 2 2 3 3 3 3 3 3 3
2 2 3 1 1 1 3
2 2 3 1 1 3
A A 1 1
B A A B C C
B A A A B C C
B B B B B C C C C C C C
#22. Move B:
2 2 2 2 2 3 3 3 3 3 3 3
A 2 A 2 3 1 1 1 3
A 2 A 2 3 1 1 3
A A A 1 1
B B C C
B B C C
B B B B B C C C C C C C
#23. Move 2:
3 3 3 3 3 3 3
3 1 1 1 3
3 1 1 3
2 2 2 2 2 1 1
A 2 A B 2 B C C
A 2 A B 2 B C C
A A A B B B B B C C C C C C C
#24. Move 3:
3 3 3 3 3 3 3
3 3
3 3
2 2 2 2 2 1 1 1
A 2 A B 2 B C 1 1 C
A 2 A B 2 B C 1 1 C
A A A B B B B B C C C C C C C
#25. Move 1:
3 3 3 3 3 3 3
3 3 1 1 1
3 3 1 1
2 2 2 2 2 1 1
A 2 A B 2 B C C
A 2 A B 2 B C C
A A A B B B B B C C C C C C C
#26. Move 2:
3 3 3 3 3 3 3
3 2 2 2 2 2 3 1 1 1
3 2 2 3 1 1
2 2 1 1
A A B B C C
A A B B C C
A A A B B B B B C C C C C C C
#27. Move A:
A A 3 3 3 3 3 3 3
A A 3 2 2 2 2 2 3 1 1 1
A A A 3 2 2 3 1 1
2 2 1 1
B B C C
B B C C
B B B B B C C C C C C C
#28. Move B:
A A 3 3 3 3 3 3 3
B A A B 3 2 2 2 2 2 3 1 1 1
B A A A B 3 2 2 3 1 1
B B B B B 2 2 1 1
C C
C C
C C C C C C C
#29. Move C:
A A 3 3 3 3 3 3 3
B A A B 3 2 2 2 2 2 3 1 1 1
B A A A B 3 2 2 3 1 1
B B B B B 2 2 1 1
C C
C C
C C C C C C C
#30. Move 1:
A A 3 3 3 3 3 3 3
B A A B 3 2 2 2 2 2 3
B A A A B 3 2 1 1 1 2 3
B B B B B 2 1 1 2
C C 1 1
C C
C C C C C C C
#31. Move A:
3 3 3 3 3 3 3
3 2 2 2 2 2 3
A A 3 2 1 1 1 2 3
B A A B 2 1 1 2
C B A A A B C 1 1
C B B B B B C
C C C C C C C