A brief history of puzzles...
by Prof. David Joyner
Mankind has been fascinated with puzzles of one type or another since
antiquity. Different types of puzzles include (see [vDB], [SB] for references):
- Construction or packing puzzles (such as burr puzzles (see also
puzzle site), soma
cube puzzles, polyomino puzzles,
or certain interlocking puzzles),
- moving piece puzzles (such as jigsaw puzzles or tanagrams),
- dissection puzzles (such as those of S.
Loyd and H.
E Dudeney, for example),
- sequential movement puzzles (such as the 15 puzzle, the Rubik's
cube and Orbix Puzzle -
- wire and string puzzles (such the Chinese ring puzzle - these are in fact
sequential movement puzzles in disguise; see also Livewire for some examples),
- positioning puzzles (such as peg solitaire, shunting problems, and sliding
- graph-theoretic puzzles (such as mazes,
insanity, and the Icosian puzzle described below)
- number and logic puzzles,
- chess puzzles (such as retro and other puzzles derived from games),
- folding puzzles and other puzzles associated with magic tricks,
- word puzzles (such as crossword puzzles or anagram puzzles).
This page shall restricted to a brief history of some
sequential puzzles. As mentioned, puzzles have been around for a long
time. For example, David
Singmaster, one of the authorities on the history of such puzzles, gives a
reference that suggests the Chinese rings puzzle may have originated in China as
early as the second century AD. However, it appears to be unknown when they were
discovered or even in what country.
More history is available in David Singmaster's excellent "Afterward"
(chapter 7) in [R].
- Around 1550 Cardan, an Italian mathematician specializing in the theory of
algebraic equations (he discovered the cubic analog of the quadratic formula
for the roots of a polynomial), described the Chinese ring puzzle (called
Cardan's rings in [UStA]):
- In 1857 W. Hamilton (1805-1865), an Irish mathematician perhaps best known
for his discovery of the quaternion numbers, invented the Icosian puzzle. The
idea of this puzzle is to find a tour of the 12 vertices of an icosahedron
which visits each vertex exactly once.
- In the early 1870's there appeared the famous 15 puzzle. Though some
accounts state that this puzzle was discovered by Sam Loyd, the American
problem and puzzle inventor, otehre authorities dispute this. However, there
is less dispute that he invented the "14-15 puzzle":
This puzzle was extremely
popular around the early 1900's.
- In 1883 É. Lucas (1843-1891), a French mathematician specializing in the
theory of numbers, invented the Tower of Hanoi puzzle. This puzzle has three
pegs and a number of disks of increasing size with a hole drilled in the
center so they may be placed over any one of the pegs:
The solution of this
puzzle has a very interesting mathematical explanation [G].
- In the early 1920's P. MacMahon (1854-1929), a British mathematician and
Naval Officer specializing in combinatorics, invented the 30 colored cube
puzzle - marketed under the name Mayblox. One can color a cube with 6 colors
in 30 ways (not counting rotations of course). These 30 cubes are all that's
given. There are several puzzles one can formulte regarding these blocks. One
is to try to make a 3x3x3 cube where two cube can touch at a face only if the
faces have the same color.
- In the early 1970's U. Meffert, an engineer and inventor, invented the
Pyraminx (a "Rubik's tetrahedron") Mechanism and his patent covers all puzzles
using 4 or more none orthogonal axis. This includes the Tetraminx, Skewb, and
Megaminx Puzzle Balls.
- In the mid 1970's E. Rubik, a Professor in the Department of Graphics
Design at the University of Budapest, invented the Rubik's cube. During the
Rubik's cube craze in the 1980's close to 100 million cubes were sold. The
solution of this puzzle has a very interesting mathematical explanation [S2].
- A communication from Christoph Bandelow tells the following very
interesting history (which I have slightly edited) of the megaminx/magic
"...there were at least half a dozen of people or groups of people who have
- within a few weeks in 1981 - filed a patent application for the Magic
Dodecahedron. The patent attorney Moll filed only a "Gebrauchsmuster" without
giving any technical details. This did not have any consequences. My own
patent application however (jointly with Helmut Corbeck, a student whom I had
asked to make the final drawings for me) did have consequences. It was bought
by ARXON (the German division of Ideal Toy). Together with Ideal Toy France
and Ideal Toy Britain, ARXON organized the production of our dodecahedron in
Hungary. Of course, Hungarian engineers still had to work out many details of
the production and assembling. At nearly the same time, but a few weeks later
and completely independently, Uwe Meffert got his impulse from Kersten Meier
and Udo Krell which finally led to the production of the Megaminxes in Hong
- In the 1980's a puzzle called Merlin's magic square was invented. In this
puzzle, played on a square grid of points, a "move" is to pick a vertex on the
grid. Once a point is picked, it has the effect of "turning on" all the
neighboring points joined to it by a single edge in the grid graph. The object
is to "turn on" all the points. The solution of this has an interesting
mathematical description [P], [V].
- In the 1990's a puzzle called The Orbix,
an analog of the Merlin's magic square, was invented. The square
grid used in Merlin's magic square is replaced by the graph
of the vertices and edges of an icosahedron.
- One of the most interesting recently invented puzzles is the Masterball.
It was invented by Dr. Geza Gyovai, a 46 year old Hungarian-born engineer and
lawyer now living in Zurich, Switzerland. It seems to be related to the
"hockeypuck" invented by A. Vegh [R], but is more complicated in several ways.
[vDB] P. van Delft and J. Botermans, Creative puzzles of the world,
Harry A. Abrams, Pub., New York, 1978
[G] M. Gardner, "The binary Gray code", in Knotted donuts and other
mathematical entertainments, F. H. Freeman and Co., NY, 1986
[P] D. Pelletier, "Merlins magic square", American Math. Monthly,
[R] E. Rubik et al, Rubik's cubic compendium, Oxford Univ. Press, 1987
Singmaster, Queries on "Sources in Recreational Mathematics", 1995, 22pp.
[S2] ----, Notes on Rubiks magic cube, Enslow Publ., NJ, 1982
[SB] J. Slocum and J. Botermans, The book of ingenious and diabolical
puzzles, Times Books, New York, 1994
of St. Andrews "Mathematical games and recreations" by John J OConnor and
Edmund F Robertson
[V] S. Vajda, Mathematical games and how you play them, Ellis Horwood,
New York, 1992