title: Naturen
Mutilated chessboard problem
Scientific American
Graham's number
Rep-tile
Martin Gardner
Sol Butler
Golomb coding
Golomb sequence
Powerful number
sentences: Naturen (English: The Nature ) is a Norwegian popular science magazine, which has been published since 1877 in Bergen, Norway.
 It is the earliest still running popular science magazine of the country.
The mutilated chessboard problem is a tiling puzzle proposed by philosopher Max Black in his book "Critical Thinking" (1946).
 It was later discussed by Solomon W. Golomb (1954), and by Martin Gardner in his "Scientific American" column "Mathematical Games".
 The problem is as follows:
Scientific American (informally abbreviated SciAm) is an American popular science magazine.
 Many famous scientists, including Albert Einstein, have contributed articles in the past 170 years.
 It is the oldest continuously published monthly magazine in the United States(though it only became monthly in 1921).
Graham's number is an enormous number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory.
 It is named after mathematician Ronald Graham, who used the number as a simplified explanation of the upper bounds of the problem he was working on in conversations with popular science writer Martin Gardner.
 Gardner later described the number in "Scientific American" in 1977, introducing it to the general public.
 At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof.
 The number was published in the 1980 "Guinness Book of World Records", adding to its popular interest.
 Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem.
 Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number derived have since been proven to be valid.
In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape.
 The term was coined as a pun on animal reptiles by the American mathematician Solomon W. Golomb, who used it to describe self-replicating tilings.
 In 2012 a generalization of rep-tiles called self-tiling tile sets was introduced by Lee Sallows in "Mathematics Magazine".
Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.
 He was considered a leading authority on Lewis Carroll. "
The Annotated Alice", which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies.
 He had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century.
 He was considered the dean of American puzzlers.
 He was a prolific and versatile author, publishing more than 100 books.
Solomon W. Butler (March 3, 1895 – December 1, 1954) was a multi-talented athlete who competed in American football and track and field.
 He finished seventh in the long jump competition at the 1920 Summer Olympics.
 He also played in the National Football League for the Hammond Pros, Akron Pros, Canton Bulldogs, Buffalo Bisons, and Rock Island Independents.
 Butler is buried at Maple Grove Cemetery in Wichita, Kansas.
 Referenced sometimes as Edward Solomon Butler, was a name used by alternate people to gain notoriety off the exploits of Solomon W. Butler in various parts of the country.
Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s.
 Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code, making Golomb coding highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values.
In mathematics, the Golomb sequence, named after Solomon W. Golomb (but also called Silverman's sequence), is a non-decreasing integer sequence where "a" is the number of times that "n" occurs in the sequence, starting with "a" = 1, and with the property that for "n" > 1 each "a" is the unique integer which makes it possible to satisfy the condition.
 For example, "a" = 1 says that 1 only occurs once in the sequence, so "a" cannot be 1 too, but it can be, and therefore must be, 2.
 The first few values are
A powerful number is a positive integer "m" such that for every prime number "p" dividing "m", "p" also divides "m".
 Equivalently, a powerful number is the product of a square and a cube, that is, a number "m" of the form "m" = "a""b", where "a" and "b" are positive integers.
 Powerful numbers are also known as squareful, square-full, or 2-full.
 Paul Erdős and George Szekeres studied such numbers and Solomon W. Golomb named such numbers "powerful".

Question: Question: What is the name of an American popular science magazine that included a discussion by Solomon W. Golomb and Martin Gardner on mutilated chessboard problem? 

 Your answer will be verified with exact match score. To ensure correct verification, only provide the answer within the <answer> </answer> tags. Do not put any sentences or reasoning process within the <answer> </answer> tags. 

Supporting Information: Paragraph 0 

 Naturen (English: The Nature ) is a Norwegian popular science magazine, which has been published since 1877 in Bergen, Norway.
 It is the earliest still running popular science magazine of the country. 

--------------------------------

Paragraph 1 

 The mutilated chessboard problem is a tiling puzzle proposed by philosopher Max Black in his book "Critical Thinking" (1946).
 It was later discussed by Solomon W. Golomb (1954), and by Martin Gardner in his "Scientific American" column "Mathematical Games".
 The problem is as follows: 

--------------------------------

Paragraph 2 

 Scientific American (informally abbreviated SciAm) is an American popular science magazine.
 Many famous scientists, including Albert Einstein, have contributed articles in the past 170 years.
 It is the oldest continuously published monthly magazine in the United States(though it only became monthly in 1921). 

--------------------------------

Paragraph 3 

 Graham's number is an enormous number that arises as an upper bound on the answer of a problem in the mathematical field of Ramsey theory.
 It is named after mathematician Ronald Graham, who used the number as a simplified explanation of the upper bounds of the problem he was working on in conversations with popular science writer Martin Gardner.
 Gardner later described the number in "Scientific American" in 1977, introducing it to the general public.
 At the time of its introduction, it was the largest specific positive integer ever to have been used in a published mathematical proof.
 The number was published in the 1980 "Guinness Book of World Records", adding to its popular interest.
 Other specific integers (such as TREE(3)) known to be far larger than Graham's number have since appeared in many serious mathematical proofs, for example in connection with Harvey Friedman's various finite forms of Kruskal's theorem.
 Additionally, smaller upper bounds on the Ramsey theory problem from which Graham's number derived have since been proven to be valid. 

--------------------------------

Paragraph 4 

 In the geometry of tessellations, a rep-tile or reptile is a shape that can be dissected into smaller copies of the same shape.
 The term was coined as a pun on animal reptiles by the American mathematician Solomon W. Golomb, who used it to describe self-replicating tilings.
 In 2012 a generalization of rep-tiles called self-tiling tile sets was introduced by Lee Sallows in "Mathematics Magazine". 

--------------------------------

Paragraph 5 

 Martin Gardner (October 21, 1914May 22, 2010) was an American popular mathematics and popular science writer, with interests also encompassing scientific skepticism, micromagic, philosophy, religion, and literature—especially the writings of Lewis Carroll, L. Frank Baum, and G. K. Chesterton.
 He was considered a leading authority on Lewis Carroll. "
The Annotated Alice", which incorporated the text of Carroll's two Alice books, was his most successful work and sold over a million copies.
 He had a lifelong interest in magic and illusion and was regarded as one of the most important magicians of the twentieth century.
 He was considered the dean of American puzzlers.
 He was a prolific and versatile author, publishing more than 100 books. 

--------------------------------

Paragraph 6 

 Golomb coding is a lossless data compression method using a family of data compression codes invented by Solomon W. Golomb in the 1960s.
 Alphabets following a geometric distribution will have a Golomb code as an optimal prefix code, making Golomb coding highly suitable for situations in which the occurrence of small values in the input stream is significantly more likely than large values. 

--------------------------------

Paragraph 7 

 In mathematics, the Golomb sequence, named after Solomon W. Golomb (but also called Silverman's sequence), is a non-decreasing integer sequence where "a" is the number of times that "n" occurs in the sequence, starting with "a" = 1, and with the property that for "n" > 1 each "a" is the unique integer which makes it possible to satisfy the condition.
 For example, "a" = 1 says that 1 only occurs once in the sequence, so "a" cannot be 1 too, but it can be, and therefore must be, 2.
 The first few values are 

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Answer: Scientific American