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Concept
42 (number)
Summary
42 (forty-two) is the natural number that follows 41 and precedes 43.
Forty-two (42) is a pronic number and an abundant number; its prime factorization () makes it the second sphenic number and also the second of the form ().
Additional properties of the number 42 include:
It is the number of isomorphism classes of all simple and oriented directed graphs on 4 vertices. In other words, it is the number of all possible outcomes (up to isomorphism) of a tournament consisting of 4 teams where the game between any pair of teams results in three possible outcomes: the first team wins, the second team wins, or there is a draw. The group stage of the FIFA World cup is a good example.
It is the third primary pseudoperfect number.
It is a Catalan number. Consequently, 42 is the number of noncrossing partitions of a set of five elements, the number of triangulations of a heptagon, the number of rooted ordered binary trees with six leaves, the number of ways in which five pairs of nested parentheses can be arranged, etc.
It is an alternating sign matrix number, that is, the number of 4-by-4 alternating sign matrices.
It is the smallest number k that is equal to the sum of the nonprime proper divisors of k, i.e., 42 = 1 + 6 + 14 + 21.
It is the number of partitions of 10—the number of ways of expressing 10 as a sum of positive integers (note a different sense of partition from that above).
1111123, one of the 42 unordered integer partitions of 10 has 42 ordered compositions, since 7!/5!=42.
The angle of 42 degrees can be constructed with only compass and straight edge and using the golden ratio in 18 degree, i.e. the difference between constructible angles 60 and 18.
Given 27 same-size cubes whose nominal values progress from 1 to 27, a 3 × 3 × 3 magic cube can be constructed such that every row, column, and corridor, and every diagonal passing through the center, is composed of three numbers whose sum of values is 42.
It is the third pentadecagonal number. It is a meandric number and an open meandric number.
Official source
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