hard Set 35 Logic Puzzle

Tower of Hanoi: 2 Disks — Hard #35

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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 (largest) 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."}]

Title
Tower of Hanoi: 2 Disks — Hard #35
DiskCount
2
TaskType
count-moves
Pegs
A: Peg A (Start)
B: Peg B (Spare)
C: Peg C (Goal)
InitialState
A: [2,1]
B: []
C: []
TargetState
A: []
B: []
C: [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 (largest) 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."}
OptimalMoveCount
3
Question
Without solving step-by-step, calculate the minimum number of moves needed to transfer 2 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.