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):
This page shall restricted to a brief history of some sequential puzzles.
- Construction or packing puzzles (such as burr puzzles (see also IBM's burr 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. Ernest Dudeney, for example),
- sequential movement puzzles (such as the 15 puzzle, the Rubik's cube and the Orbix puzzle - see below),
- 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 block puzzles),
- graph-theoretic puzzles (such as mazes, instant 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).
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 Uwe 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 dodecahedron:
"...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 Kong."
- 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, "Merlin's magic square", American Math. Monthly, 94(1987)143-150
[R] E. Rubik et al, Rubik's cubic compendium, Oxford Univ. Press, 1987
[S1] David Singmaster, Queries on "Sources in Recreational Mathematics", 1995, 22pp.
[S2] ----, Notes on Rubik's magic cube, Enslow Publ., NJ, 1982 [SB] J. Slocum and J. Botermans, The book of ingenious and diabolical puzzles, Times Books, New York, 1994
[UStA] University of St. Andrews "Mathematical games and recreations" by John J O'Connor and Edmund F Robertson
[V] S. Vajda, Mathematical games and how you play them, Ellis Horwood, New York, 1992
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