Tower Of Hanoi Hanoi 4disc Hard — Set 21

Tower of Hanoi: 4 Disks — Hard #21

Title

Tower of Hanoi: 4 Disks — Hard #21

DiskCount

4

TaskType

count-moves

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]

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

Without solving step-by-step, calculate the minimum number of moves needed to transfer 4 disks from peg A to peg C. Write the formula and the answer.

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

Use the formula: minimum moves = 2ⁿ − 1, where n is the disk count.