Tower Of Hanoi Hanoi 6disc Hard — Set 92

Tower of Hanoi: 6 Disks — Hard #92

Title

Tower of Hanoi: 6 Disks — Hard #92

DiskCount

6

TaskType

count-moves

Pegs

A: Peg A (Start)

B: Peg B (Spare)

C: Peg C (Goal)

InitialState

A: [6,5,4,3,2,1]

B: []

C: []

TargetState

A: []

B: []

C: [6,5,4,3,2,1]

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 (medium) 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 (medium) 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 (medium) 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."}
• {"step":16,"from":"A","to":"B","diskSize":5,"description":"Move disk 5 (second largest) from peg A to peg B."}
• {"step":17,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":18,"from":"C","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg B."}
• {"step":19,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":20,"from":"C","to":"A","diskSize":3,"description":"Move disk 3 (medium) from peg C to peg A."}
• {"step":21,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
• {"step":22,"from":"B","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg A."}
• {"step":23,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":24,"from":"C","to":"B","diskSize":4,"description":"Move disk 4 (medium) from peg C to peg B."}
• {"step":25,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":26,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."}
• {"step":27,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
• {"step":28,"from":"A","to":"B","diskSize":3,"description":"Move disk 3 (medium) from peg A to peg B."}
• {"step":29,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":30,"from":"C","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg B."}
• {"step":31,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":32,"from":"A","to":"C","diskSize":6,"description":"Move disk 6 (largest) from peg A to peg C."}
• {"step":33,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
• {"step":34,"from":"B","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg A."}
• {"step":35,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":36,"from":"B","to":"C","diskSize":3,"description":"Move disk 3 (medium) from peg B to peg C."}
• {"step":37,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":38,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."}
• {"step":39,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
• {"step":40,"from":"B","to":"A","diskSize":4,"description":"Move disk 4 (medium) from peg B to peg A."}
• {"step":41,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":42,"from":"C","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg B."}
• {"step":43,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":44,"from":"C","to":"A","diskSize":3,"description":"Move disk 3 (medium) from peg C to peg A."}
• {"step":45,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
• {"step":46,"from":"B","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg A."}
• {"step":47,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":48,"from":"B","to":"C","diskSize":5,"description":"Move disk 5 (second largest) from peg B to peg C."}
• {"step":49,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":50,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."}
• {"step":51,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
• {"step":52,"from":"A","to":"B","diskSize":3,"description":"Move disk 3 (medium) from peg A to peg B."}
• {"step":53,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":54,"from":"C","to":"B","diskSize":2,"description":"Move disk 2 (second smallest) from peg C to peg B."}
• {"step":55,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":56,"from":"A","to":"C","diskSize":4,"description":"Move disk 4 (medium) from peg A to peg C."}
• {"step":57,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}
• {"step":58,"from":"B","to":"A","diskSize":2,"description":"Move disk 2 (second smallest) from peg B to peg A."}
• {"step":59,"from":"C","to":"A","diskSize":1,"description":"Move disk 1 (smallest) from peg C to peg A."}
• {"step":60,"from":"B","to":"C","diskSize":3,"description":"Move disk 3 (medium) from peg B to peg C."}
• {"step":61,"from":"A","to":"B","diskSize":1,"description":"Move disk 1 (smallest) from peg A to peg B."}
• {"step":62,"from":"A","to":"C","diskSize":2,"description":"Move disk 2 (second smallest) from peg A to peg C."}
• {"step":63,"from":"B","to":"C","diskSize":1,"description":"Move disk 1 (smallest) from peg B to peg C."}

OptimalMoveCount

63

Question

Without solving step-by-step, calculate the minimum number of moves needed to transfer 6 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.