Mathematical Recreations and Essays

ARITHEMETICAL RECREATIONS
To find a number selected by someone
Prediction of the result of certain operations
Problems involving two numbers
Problems depending on the scale of notation
Other problems with numbers in the denary scale
Four fours problems
Problems with a series of numbered things
Arithmetical restorations
Calendar problems
Medieval problems in arithmetic
The Josephus problem. Decimation
Nim and similar games
Moore's game
Kayles
Wythoff's game
Addendum on solutions
II ARITHEMETICAL RECREATIONS (continued)
Arithmetical fallacies
Paradoxical problems
Probability problems
Permutation problems
Bachet's weights problem
The decimal expression for 1/n
Decimals and continued fractions
Rational right-angled triangles
Triangular and pyramidal numbers
Divisibility
The prime number theorem
Mersenne numbers
Perfect numbers
Fermat numbers
Fermat's Last Theorem
Galois fields
III GEOMETRICAL RECREATIONS
Geometrical fallacies
Geometrical paradoxes
Continued fractions and lattice points
Geometrical dissections
Cyclotomy
Compass problems
The five-disc problem
Lebesgue's minimal problem
Kakeya's minimal problem
Addendum on a solution
IV GEOMETRICAL RECREATIONS (continued)
Statical games of position
Three-in-a-row. Extension to p-in-a-row
Tessellation
Anallagmatic pavements
Polyominoes
Colour-cube problem
Squaring the square
Dynamical games of position
Shunting problems
Ferry-boat problems
Geodesic problems
Problems with counters or pawns
Paradromic rings
Addendum on solutions
V POLYHEDRA
Symmetry and symmetries
The five Platonic solids
Kepler's mysticism
"Pappus, on the distribution of vertices"
Compounds
The Archimedean solids
Mrs. Stott's construction
Equilateral zonohedra
The Kepler-Poinsot polyhedra
The 59 icosahedra
Solid tessellations
Ball-piling or close-packing
The sand by the sea-shore
Regular sponges
Rotating rings of tetrahedra
The kaleidoscope
VI CHESS-BOARD RECREATIONS
Relative value of pieces
The eight queens problem
Maximum pieces problem
Minimum pieces problem
Re-entrant paths on a chess-board
Knight's re-entrant path
King's re-entrant path
Rook's re-entrant path
Bishop's re-entrant path
Route's on a chess-board
Guarini's problem
Latin squares
Eulerian squares
Euler's officers problem
Eulerian cubes
VII MAGIC SQUARE
Magic squares of an odd order
Magic squares of a singly-even order
Magic squares of a doubly-even order
Bordered squares
Number of squares of a given order
Symmetrical and pandiagonal squares
Generalization of De la LoubÅ re's rule
Arnoux's method
Margossian's method
Magic squares of non-consecutive numbers
Magic squares of primes
Doubly-magic and trebly-magic squares
Other magic problems
Magic domino squares
Cubic and octahedral dice
Interlocked hexagons
Magic cubes
VIII MAP-COLOURING PROBLEMS
The four-colour conjecture
The Petersen graph
Reduction to a standard map
Minimum number of districts for possible failure
Equivalent problem in the theory of numbers
Unbounded surfaces
Dual maps
Maps on various surfaces
"Pits, peaks, and passes"
Colouring the icosahedron
IX UNICURSAL PROBLEMS
Euler's problem
Number of ways of describing a unicursal figure
Mazes
Trees
The Hamiltonian game
Dragon designs
X COMBINATORIAL DESIGNS
A projective plane
Incidence matrices
An Hadamard matrix
An error-corrrecting code
A block design
Steiner triple systems
Finite geometries
Kirkman's school-girl problem
Latin squares
The cube and the simplex
Hadamard matrices
Picture transmission
Equiangular lines in 3-space
Lines in higher-dimensional space
C-matrices
Projective planes
XI MISCELLANEOUS
The fifteen puzzle
The Tower of Hano‹
Chinese rings
Problems connected with a pack of cards
Shuffling a pack
Arrangements by rows and columns
Bachet's problem with pairs of cards
Gergonne's pile problem
The window reader
The mouse trap. Treize
XII THREE CLASSICAL GEOMETRICAL PROBLEMS
The duplication of the cube
"Solutions by Hippocrates, Archytas, Plato, Menaechmus, Apollonius, and Diocles"
"Solutions by Vieta, Descartes, Gregory of St. Vincent, and Newton"
The trisection of an angle
"Solutions by Pappus, Descartes, Newton, Clairaut, and Chasles"
The quadrature of the circle
Origin of symbo p
Geometrical methods of approximation to the numerical value of p
"Results of Egyptians, Babylonians, Jews"
Results of Archimedes and other Greek writers
"Results of European writers, 1200-1630"
Theorems of Wallis and Brouncker
"Results of European writers, 1699-1873"
Approximation by the theory of probability
XIII CALCULATING PRODIGIES
"John Wallis, 1616-1703"
"Buxton, circ. 1707-1772"
"Fuller, 1710-1790; AmpÅ re"
"Gauss, Whately"
"Colburn, 1804-1840"
"Bidder, 1806-1878"
"Mondeux, Mangiamele"
"Dase, 1824-1861"
"Safford, 1836-1901"
"Zamebone, Diamandi, Rckle"
"Inaudi, 1867"
Types of memory of numbers
Bidder's analysis of methods usesd
Multiplication
Digital method for division and factors
Square roots. Higher roots
Compound interest
Logarithms
Alexander Craig Aitken
XIV CRYPTOGRAPHY AND CRYPTANALYSIS
Cryptographic systems
Transposition systems
Columnar transposition
Digraphs and trigraphs
Comparision of several messages
The grille
Substitution systems
Tables of frequency
Polyalphabetic systems
The VigenÅ re square
The Playfair cipher
Code
Determination of cryptographic system
A few final remarks
Addendum: References for further study
INDEX