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Verbal arithmetic, also known as alphametics, cryptarithmetic, cryptarithm or word addition, is a type of mathematical game consisting of a mathematical equation among unknown numbers, whose digits are represented by letters of the alphabet. The goal is to identify the value of each letter.
3 + 2 = 5 with apples, a popular choice in textbooks [1] Addition (usually signified by the plus symbol +) is one of the four basic operations of arithmetic, the other three being subtraction, multiplication, and division. [2] The addition of two whole numbers results in the total amount or sum of those values combined. The example in the ...
The proof is difficult to follow but marks a turning point in the word problem for groups. [3]: 342 1955 (): Pyotr Novikov gives the first published proof that the word problem for groups is unsolvable, using Turing's cancellation semigroup result. [17] [3]: 354 The proof contains a "Principal Lemma" equivalent to Britton's Lemma.
The four color theorem and optimal sphere packing were two major problems of discrete mathematics solved in the second half of the 20th century. [44] The P versus NP problem , which remains open to this day, is also important for discrete mathematics, since its solution would potentially impact a large number of computationally difficult problems.
An edge coloring with k colors is called a k-edge-coloring and is equivalent to the problem of partitioning the edge set into k matchings. The smallest number of colors needed for an edge coloring of a graph G is the chromatic index, or edge chromatic number, χ ′ (G). A Tait coloring is a 3-edge coloring of a cubic graph.
Color printing: By at least the Yuan dynasty, China had invented color printing for paper. British art historian Michael Sullivan writes that "the earliest color printing known in China, and indeed in the whole world, is a two-color frontispiece to a Buddhist sutra scroll, dated 1346".