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A vanishing puzzle is a
Wemple & Company marketed an advertising card named ''The Magic Egg Puzzle, (How Many Eggs?)'' in New York in 1880. Cutting the rectangular card into four oblongs allowed the pieces to be rearranged to show either 8, 9 or 10 eggs. Many other similar puzzles have been published since.
Chess player and recreational mathematician 
Prizes from $5 to $100 were offered for the best explanation of one illusion. Though the names of the winners were published, their explanations were not.
Missing_square_puzzle-AB.svg, Both "total triangles" are in a perfect 13×5 grid; and both the "component triangles", the blue in a 5×2 grid and the red in an 8×3 grid
Loyd64-65-dis b.svg,
A vanishing puzzle is a mechanical
Mechanical may refer to:
Machine
* Machine (mechanical), a system of mechanisms that shape the actuator input to achieve a specific application of output forces and movement
* Mechanical calculator, a device used to perform the basic operations of ...
optical illusion
Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual perception, percept that arguably appears to differ from reality. Illusions come in a wide v ...
comprising multiple pieces which can be rearranged to show different versions of a picture depicting several objects, the number of which depending on the arrangement of the pieces.
History
Wemple & Company marketed an advertising card named ''The Magic Egg Puzzle, (How Many Eggs?)'' in New York in 1880. Cutting the rectangular card into four oblongs allowed the pieces to be rearranged to show either 8, 9 or 10 eggs. Many other similar puzzles have been published since.
Chess player and recreational mathematician Sam Loyd
Samuel Loyd (January 30, 1841 – April 10, 1911), was an American chess player, chess composer, puzzle author, and recreational mathematics, recreational mathematician. Loyd was born in Philadelphia but raised in New York City.
As a chess com ...
patented rotary vanishing puzzles in 1896 and published versions named ''Get Off the Earth'', ''Teddy and the Lion'' and ''The Disappearing Bicyclist'' (pictured). Each had a circular card connected to a cardboard backdrop with a pin, letting it freely rotate. In ''The Disappearing Bicyclist'', when the disc is rotated such that the arrow points to A, 13 boys can be counted, but when it points to B, there are only 12 boys.
Prizes from $5 to $100 were offered for the best explanation of one illusion. Though the names of the winners were published, their explanations were not.
Similar puzzles
Themissing square puzzle
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. ...
is an optical illusion
Within visual perception, an optical illusion (also called a visual illusion) is an illusion caused by the visual system and characterized by a visual perception, percept that arguably appears to differ from reality. Illusions come in a wide v ...
used in mathematics
Mathematics is an area of knowledge that includes the topics of numbers, formulas and related structures, shapes and the spaces in which they are contained, and quantities and their changes. These topics are represented in modern mathematics ...
classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. It depicts two arrangements made of similar shapes in slightly different configurations. Each apparently forms a 13×5 right-angled triangle
A triangle is a polygon with three Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC.
In Euclidean geometry, an ...
, but one has a 1×1 hole in it.
Sam Loyd
Samuel Loyd (January 30, 1841 – April 10, 1911), was an American chess player, chess composer, puzzle author, and recreational mathematics, recreational mathematician. Loyd was born in Philadelphia but raised in New York City.
As a chess com ...
's paradoxical dissection
Missing square edit.gif, A variant of Mitsunobu Matsuyama's "paradox"
Sam Loyd
Samuel Loyd (January 30, 1841 – April 10, 1911), was an American chess player, chess composer, puzzle author, and recreational mathematics, recreational mathematician. Loyd was born in Philadelphia but raised in New York City.
As a chess com ...
's chessboard paradox
The chessboard paradoxGreg N. Frederickson: ''Dissections: Plane and Fancy''. Cambridge University Press, 2003, , chapter 23, pp. 268–277 in particular pp. 271–274 Colin Foster: "Slippery Slopes". In: ''Mathematics in School'', vol. 34, no. 3 ...
demonstrates two rearrangements of an 8×8 square. In the "larger" rearrangement (the 5×13 rectangle in the image to the right), the gaps between the figures have a combined unit square more area than their square gaps counterparts, creating an illusion that the figures there take up more space than those in the original square figure.
See also
*Missing square puzzle
The missing square puzzle is an optical illusion used in mathematics classes to help students reason about geometrical figures; or rather to teach them not to reason using figures, but to use only textual descriptions and the axioms of geometry. ...
* Chessboard paradox
The chessboard paradoxGreg N. Frederickson: ''Dissections: Plane and Fancy''. Cambridge University Press, 2003, , chapter 23, pp. 268–277 in particular pp. 271–274 Colin Foster: "Slippery Slopes". In: ''Mathematics in School'', vol. 34, no. 3 ...
* Einstellung effect
Einstellung () is the development of a mechanized state of mind. Often called a problem solving set, Einstellung refers to a person's predisposition to solve a given problem in a specific manner even though better or more appropriate methods of so ...
* Hooper's paradox
Hooper's paradox is a falsidical paradox based on an optical illusion. A geometric shape with an area of 32 units is dissected into four parts, which afterwards get assembled into a rectangle with an area of only 30 units.
Explanation
Upon close ...
* Missing dollar riddle
The missing dollar riddle is a famous riddle that involves an informal fallacy. It dates to at least the 1930s, although similar puzzles are much older.
Statement
Although the wording and specifics can vary, the puzzle runs along these lines:
...
References
{{DEFAULTSORT:Vanishing Puzzle Optical illusions Mathematical paradoxes Recreational mathematics Logic puzzles Geometric dissection