The Tower of Hanoi, a puzzle dating back to 1883, remains a fixture in both popular culture and academic pursuits. Governed by two fundamental rules, the puzzle challenges players to move discs between rods. Only one disc may be moved at a time, and no larger disc can be placed atop a smaller one. The discs, ascending in size from bottom to top, present a compelling challenge, with numerous strategies for completion. Conquering this puzzle marks one as a mathematical adept. Difficulty scales…