hard Set 95 Logic Puzzle

Tower of Hanoi: 4 Disks — Hard #95

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[{"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 — Hard #95
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.