You have three small poles and five hoops - XS, S, M, L, XL (as in extra small, small, medium, large and extra large). They are placed on pole 1 in order, with largest at the bottom.

You can move one hoop at a time, and the hoops you are not moving have to be on a pole. You also cannot place a hoop on top of a smaller one. How can you move the hoops so that they are in the same order as they are now, but on pole 3?

(In reply to Stacks by DJ)

DECLARE SUB display ()
DECLARE SUB transfer (n!, source!, dest!)
DIM SHARED pole$(3), n
INPUT "Number of hoops:", n
FOR i = 1 TO n
  pole$(1) = CHR$(64 + i) + pole$(1)
NEXT
transfer n, 1, 3

SUB display
  FOR i = n TO 1 STEP -1
    FOR p = 1 TO 3
      IF LEN(pole$(p)) < i THEN
        PRINT \" | \";
      ELSE
        PRINT \" \"; MID$(pole$(p), i, 1); \" \";
      END IF
    NEXT
    PRINT
  NEXT
END SUB

SUB transfer (n, source, dest)
  IF n = 1 THEN
    PRINT \"Move A from\"; source; \"to\"; dest
    pole$(dest) = pole$(dest) + RIGHT$(pole$(source), 1)
    pole$(source) = LEFT$(pole$(source), LEN(pole$(source)) - 1)
    display
  ELSE
    transfer n - 1, source, 6 - source - dest
    PRINT \"Move \"; CHR$(ASC(\"A\") + n - 1); \" from\"; source; \"to\"; dest
    pole$(dest) = pole$(dest) + RIGHT$(pole$(source), 1)
    pole$(source) = LEFT$(pole$(source), LEN(pole$(source)) - 1)
    display
    transfer n - 1, 6 - source - dest, dest
  END IF
END SUB

With results:
Number of hoops:4
Move A from 1 to 2
| | |
B | |
C | |
D A |
Move B from 1 to 3
| | |
| | |
C | |
D A B
Move A from 2 to 3
| | |
| | |
C | A
D | B
Move C from 1 to 2
| | |
| | |
| | A
D C B
Move A from 3 to 1
| | |
| | |
A | |
D C B
Move B from 3 to 2
| | |
| | |
A B |
D C |
Move A from 1 to 2
| | |
| A |
| B |
D C |
Move D from 1 to 3
| | |
| A |
| B |
| C D
Move A from 2 to 3
| | |
| | |
| B A
| C D
Move B from 2 to 1
| | |
| | |
| | A
B C D
Move A from 3 to 1
| | |
| | |
A | |
B C D
Move C from 2 to 3
| | |
| | |
A | C
B | D
Move A from 1 to 2
| | |
| | |
| | C
B A D
Move B from 1 to 3
| | |
| | B
| | C
| A D
Move A from 2 to 3
| | A
| | B
| | C
| | D

Number of hoops:5
Move A from 1 to 3
| | |
B | |
C | |
D | |
E | A
Move B from 1 to 2
| | |
| | |
C | |
D | |
E B A
Move A from 3 to 2
| | |
| | |
C | |
D A |
E B |
Move C from 1 to 3
| | |
| | |
| | |
D A |
E B C
Move A from 2 to 1
| | |
| | |
A | |
D | |
E B C
Move B from 2 to 3
| | |
| | |
A | |
D | B
E | C
Move A from 1 to 3
| | |
| | |
| | A
D | B
E | C
Move D from 1 to 2
| | |
| | |
| | A
| | B
E D C
Move A from 3 to 2
| | |
| | |
| | |
| A B
E D C
Move B from 3 to 1
| | |
| | |
| | |
B A |
E D C
Move A from 2 to 1
| | |
| | |
A | |
B | |
E D C
Move C from 3 to 2
| | |
| | |
A | |
B C |
E D |
Move A from 1 to 3
| | |
| | |
| | |
B C |
E D A
Move B from 1 to 2
| | |
| | |
| B |
| C |
E D A
Move A from 3 to 2
| | |
| A |
| B |
| C |
E D |
Move E from 1 to 3
| | |
| A |
| B |
| C |
| D E
Move A from 2 to 1
| | |
| | |
| B |
| C |
A D E
Move B from 2 to 3
| | |
| | |
| | |
| C B
A D E
Move A from 1 to 3
| | |
| | |
| | A
| C B
| D E
Move C from 2 to 1
| | |
| | |
| | A
| | B
C D E
Move A from 3 to 2
| | |
| | |
| | |
| A B
C D E
Move B from 3 to 1
| | |
| | |
| | |
B A |
C D E
Move A from 2 to 1
| | |
| | |
A | |
B | |
C D E
Move D from 2 to 3
| | |
| | |
A | |
B | D
C | E
Move A from 1 to 3
| | |
| | |
| | A
B | D
C | E
Move B from 1 to 2
| | |
| | |
| | A
| | D
C B E
Move A from 3 to 2
| | |
| | |
| | |
| A D
C B E
Move C from 1 to 3
| | |
| | |
| | C
| A D
| B E
Move A from 2 to 1
| | |
| | |
| | C
| | D
A B E
Move B from 2 to 3
| | |
| | B
| | C
| | D
A | E
Move A from 1 to 3
| | A
| | B
| | C
| | D
| | E

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Edited on September 9, 2003, 2:13 pm

Posted by Charlie on 2003-09-09 14:07:51