Tower of Hanoi Calculator

The Tower of Hanoi puzzle asks you to move a stack of n disks from one peg to another, one disk at a time, never placing a larger disk on a smaller one, using a third peg as a spare. The minimum number of moves is always 2ⁿ − 1, which follows by induction: moving n disks means first moving the top n − 1 disks out of the way (2ⁿ⁻¹ − 1 moves), moving the single largest disk (1 move), then moving those n − 1 disks back on top of it (2ⁿ⁻¹ − 1 moves again) — giving 2(2ⁿ⁻¹ − 1) + 1 = 2ⁿ − 1 in total.

This calculator computes 2ⁿ − 1 using arbitrary-precision integer arithmetic rather than ordinary floating-point math, so it stays exact even at n = 64 — the disk count in the popular "Tower of Brahma" legend, which needs 18,446,744,073,709,551,615 moves. Given a move rate, it also converts that move count into a human-scale duration (seconds, minutes, hours, days, or years, using a 365.25-day average year), which is how the legend's famous "hundreds of billions of years" estimate is actually derived.