{
  "title": "Tower of Hanoi minimum moves, three and four pegs",
  "description": "Minimum number of moves for the Tower of Hanoi, one row per number of disks and pegs: three pegs and four pegs, 1 to 8 disks, each found by exhaustive breadth-first search over every position (states column) and compared with 2^n - 1 (three pegs) or the Frame-Stewart recurrence (four pegs); the size of the top pile that reaches the Frame-Stewart value; and the number of different shortest move sequences. Two extra four-peg rows (10 and 21 disks, Dudeney’s cheeses) carry the Frame-Stewart value only and are marked not checked exhaustively. Computed 2026-10-31. License CC BY 4.0.",
  "license": "CC BY 4.0",
  "license_url": "https://creativecommons.org/licenses/by/4.0/",
  "creator": "Puzzles, Charts & Dilemmas",
  "page": "https://puzzleschartsanddilemmas.com/puzzles/tower-of-hanoi/",
  "derived_from": [
    "Puzzle rules as stated in Édouard Lucas, Récréations mathématiques, vol. 3 (Paris: Gauthier-Villars, 1893), p. 55, https://archive.org/details/rcrationsmat03lucauoft (public domain)",
    "Four-stool rules and the answers 33, 49 and 321 from Henry Ernest Dudeney, The Canterbury Puzzles (1907), no. 1, https://www.gutenberg.org/ebooks/27635 (public domain)"
  ],
  "method": "Compiled by Puzzles, Charts & Dilemmas from the data listed"
}