Tower Of Hanoi Hanoi 5disc Easy — Set 96

Tower of Hanoi: 5 Disks — Easy #96

Title

Tower of Hanoi: 5 Disks — Easy #96

DiskCount

5

TaskType

full-solution

Pegs

A: Peg A (Start)

B: Peg B (Spare)

C: Peg C (Goal)

InitialState

A: [5,4,3,2,1]

B: []

C: []

TargetState

A: []

B: []

C: [5,4,3,2,1]

Solution

• {"step":1,"from":"A","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg C."}
• {"step":2,"from":"A","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg B."}
• {"step":3,"from":"C","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg B."}
• {"step":4,"from":"A","to":"C","diskSize":3,"description":"Move disk 3 (medium) from peg A to peg C."}
• {"step":5,"from":"B","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg A."}
• {"step":6,"from":"B","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg C."}
• {"step":7,"from":"A","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg C."}
• {"step":8,"from":"A","to":"B","diskSize":4,"description":"Move disk 4 (second largest) from peg A to peg B."}
• {"step":9,"from":"C","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg B."}
• {"step":10,"from":"C","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg A."}
• {"step":11,"from":"B","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg A."}
• {"step":12,"from":"C","to":"B","diskSize":3,"description":"Move disk 3 (medium) from peg C to peg B."}
• {"step":13,"from":"A","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg C."}
• {"step":14,"from":"A","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg B."}
• {"step":15,"from":"C","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg B."}
• {"step":16,"from":"A","to":"C","diskSize":5,"description":"Move disk 5 (largest) from peg A to peg C."}
• {"step":17,"from":"B","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg A."}
• {"step":18,"from":"B","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg C."}
• {"step":19,"from":"A","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg C."}
• {"step":20,"from":"B","to":"A","diskSize":3,"description":"Move disk 3 (medium) from peg B to peg A."}
• {"step":21,"from":"C","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg B."}
• {"step":22,"from":"C","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg A."}
• {"step":23,"from":"B","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg A."}
• {"step":24,"from":"B","to":"C","diskSize":4,"description":"Move disk 4 (second largest) from peg B to peg C."}
• {"step":25,"from":"A","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg C."}
• {"step":26,"from":"A","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg B."}
• {"step":27,"from":"C","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg B."}
• {"step":28,"from":"A","to":"C","diskSize":3,"description":"Move disk 3 (medium) from peg A to peg C."}
• {"step":29,"from":"B","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg A."}
• {"step":30,"from":"B","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg C."}
• {"step":31,"from":"A","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg C."}

OptimalMoveCount

31

Question

Move all 5 disks from peg A to peg C, following the rules. Write out every move in order (e.g. "A→C, A→B, C→B, …").

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

The minimum number of moves required is 31 (= 25 − 1).