medium Set 20 Logic Puzzle

Tower of Hanoi: 4 Disks — Medium #20

Show solution

[{"step":1,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."},{"step":2,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."},{"step":3,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."},{"step":4,"from":"A","to":"B","diskSize":3,"description":"Move disk 3 (second largest) from peg A to peg B."},{"step":5,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."},{"step":6,"from":"C","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg B."},{"step":7,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."},{"step":8,"from":"A","to":"C","diskSize":4,"description":"Move disk 4 (largest) from peg A to peg C."},{"step":9,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."},{"step":10,"from":"B","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg A."},{"step":11,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."},{"step":12,"from":"B","to":"C","diskSize":3,"description":"Move disk 3 (second largest) from peg B to peg C."},{"step":13,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."},{"step":14,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."},{"step":15,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}]

Title
Tower of Hanoi: 4 Disks — Medium #20
DiskCount
4
TaskType
partial-continue
Pegs
A: Peg A (Start)
B: Peg B (Spare)
C: Peg C (Goal)
InitialState
A: [4,3,2,1]
B: []
C: []
TargetState
A: []
B: []
C: [4,3,2,1]
PartialState
A: [4,1]
B: [3]
C: [2]
MovesCompleted
5
Solution
  • {"step":1,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
  • {"step":2,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."}
  • {"step":3,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
  • {"step":4,"from":"A","to":"B","diskSize":3,"description":"Move disk 3 (second largest) from peg A to peg B."}
  • {"step":5,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
  • {"step":6,"from":"C","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg B."}
  • {"step":7,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
  • {"step":8,"from":"A","to":"C","diskSize":4,"description":"Move disk 4 (largest) from peg A to peg C."}
  • {"step":9,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
  • {"step":10,"from":"B","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg A."}
  • {"step":11,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
  • {"step":12,"from":"B","to":"C","diskSize":3,"description":"Move disk 3 (second largest) from peg B to peg C."}
  • {"step":13,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
  • {"step":14,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."}
  • {"step":15,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
OptimalMoveCount
15
Question
The puzzle has been started — 5 move(s) have already been made. The current state is shown below. Continue from this point and move all disks to peg C. How many more moves are needed?
Rules
  • Only one disk may be moved at a time.
  • A disk can only be placed on top of a larger disk or on an empty peg.
  • You must move the entire stack from peg A to peg C.
Hint
10 more moves are needed. The total minimum is 15.