has to piece together what actually hap-
pened by using clear and logical thinking
(thus the name).
One of the most famous logic puzzle
pioneers was writer, photographer, math-
ematician, and illustrator Charles
Lutwidge Dodgson (1832–1898), other-
wise known as Alice’s Adventures in Won-
derlandauthor Lewis Carroll. In his book
The Game of Symbolic Logiche intro-
duced several games, asking the reader to
solve a puzzle, such as: “some games are
fun,” “every puzzle is a game,” thus, “are
all puzzles fun?” Puzzles such as this are
known as syllogisms, in which the reader
is given a list of premises and asked what
can be deduced from the list. (For more
information about syllogisms, see “Foun-
dations of Mathematics.”)
What are the number of possible positionsfor a Rubik’s Cube?
Rubik’s Cube was invented in the 1970s by the Hungarian architect, inventor, and
mathematician Ernö Rubik (1944–), who also invented a number of other puzzles,
including Rubik’s Clock. The cube measures 3 by 3 by 3, with a total of 26 subcubes on
the outside. All the subcubes are hinged, making them easy to turn (by a quarter turn
in either direction) in any of the planes on the cube. Initially, each of the six sides are
painted a certain color; the object is to move the cube planes in a random way, then
return the cube so that each side has a single color again.
What are the possible number of positions of a Rubik’s cube? Mathematicians
need to use factorials (symbolized with the! sign; for more information about factori-
als, see “Algebra”) in order to find out the many iterations, as seen in the following
equation:
The number of positions turns out to be 43,252,003,274,489,856,000, or more
than 43 quintillion turns.
What is the St. Ives problem?
The St. Ives problem is one of deduction and reasoning. The centuries-old original
poem states:
!!
223
83122812
##
## #
426
The popular Rubik’s Cube puzzle requires a player to
spin sections of the cube in order to make the colors
on all six sides match. Hulton Archive/Getty Images.
