Mathematical Recreations and Essays

The classic Cambridge collection of mathematical puzzles and amusements, with arithmetical card tricks, magic squares, mazes and famous problems. A favourite source for magicians who build self-working and number-based effects.

What’s inside

1. Arithmetical recreations — Bachet, finding a chosen number, medieval problems, the Josephus problem
2. Arithmetical recreations (continued) — fallacies, permutations, Bachet’s weights, primes, Fermat’s Last Theorem
3. Geometrical recreations — geometrical fallacies and paradoxes, the map-colouring theorem
4. Geometrical recreations (continued) — three-in-a-row, tangrams, shunting and ferry-boat problems, paradromic rings
5. Mechanical recreations — paradoxes on motion, perpetual motion, sailing quicker than the wind, flight of birds
6. Chess-board recreations — the eight queens problem, the knight’s re-entrant path
7. Magic squares — their history and construction, magic stars, Euler’s officers problem
8. Bees and their cells — why the cells take the form they do
9. Unicursal problems — Euler’s problem, mazes and their history, the Hamiltonian game
10. Kirkman’s school-girls problem — its history and solutions
11. Miscellaneous problems — the Fifteen Puzzle, Tower of Hanoi, Chinese rings, shuffling, the three pile problem
12. Miscellaneous problems (continued) — digit restorations, calendar problems, dissections, compass problems
13. Calculating prodigies — Wallis, Buxton, Colburn, Bidder, Dase, Inaudi and their methods
14. Cryptographs and ciphers — the route method, the grille, the Playfair cipher, historical ciphers
15. String figures — figures from around the world and a dozen string tricks
16. Three classical geometrical problems — duplicating the cube, trisecting an angle, squaring the circle

W. W. Rouse Ball · Tenth edition, 1922 (first published 1892) · Macmillan and Co. Complete 394-page PDF. Free to download: check out at $0 and the file arrives by email and on your order page.

This classic is in the public domain. Scans come from library copies, so expect the odd stain or stamp of an old book.