What is a cryptarithmetic puzzle?
Some of the most challenging verbal
arithmetic puzzles are called cryptarith-
metic puzzles. These number puzzles
(often called cryptarithms) are made up
of mathematical equations whose digits
are represented by letters or symbols; the
goal is to identify the numerical value of
each letter. In such a puzzle, each letter
represents a unique digit, but there are
rules. As in ordinary arithmetic notation,
the leading digit of a multi-digit number
must not be zero; also, the puzzle usually
has only one solution.
Cryptarithmetic puzzles are most
often divided into two types. An alpha-
metic cryptarithm is one in which the
letters are used to represent distinct digits. These are derived from related words or
meaningful phrases in the puzzles. A digimetic cryptarithm is one in which the digits
are used to represent other digits.What are tilingand dissection puzzles?
Tiling puzzles are two-dimensional shapes that are reassembled into a larger given
shape without overlaps. The best examples of these are dissection puzzles; the most
common ones are those in which an object is converted to another by making a finite
number of cuts, then reassembling the pieces. (Most of the cuts are represented by
straight lines, but not always; in addition, sometimes the cut object can be reassem-
bled into two or more shapes.)What is a Tangram?
Some puzzle forms go back thousands of years, such as the Tangram, which is also
known as a dissection puzzle. The Tangram is of Chinese origin—literally called the
Seven-Board of Cunning—but the word itself is of English origin, and is built from
the words “tang” (thought to be a synonym for “Chinese” in the Cantonese dialect)
and “gram.” It is thought that the Pythagorean Theorem was discovered in Asia before
Pythagoras’s time with the help of Tangram pieces (for more about the Pythagorean
Theorem, see “Geometry and Trigonometry”).
The Tangram consists of a square divided into seven pieces called Tans,all of
422 which must be arranged to match particular designs, usually a square. The seven
Playing games with puzzles that often demand
mathematical skills has been a popular pastime for
generations. Hulton Archive/Getty Images.