80 (number)

80 (eighty) is the natural number following 79 and preceding 81.

In mathematics

80 is:

• the sum of Euler's totient function φ(x) over the first sixteen integers.
• a semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20 and 40) gives 80.<ref>{{#invoke:citation/CS1|citation

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• a ménage number.<ref>{{#invoke:citation/CS1|citation

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• palindromic in bases 3 (2222₃), 6 (212₆), 9 (88₉), 15 (55₁₅), 19 (44₁₉) and 39 (22₃₉).
• a repdigit in bases 3, 9, 15, 19 and 39.
• the sum of the first 4 twin prime pairs ((3 + 5) + (5 + 7) + (11 + 13) + (17 + 19)).

The Pareto principle (also known as the 80-20 rule) states that, for many events, roughly 80% of the effects come from 20% of the causes.<ref name="NYT">Template:Cite journal.</ref><ref name="8020pre">{{#invoke:citation/CS1|citation |CitationClass=web }}.</ref>

Every solvable configuration of the 15 puzzle can be solved in no more than 80 single-tile moves.<ref>A. Brüngger, A. Marzetta, K. Fukuda and J. Nievergelt, The parallel search bench ZRAM and its applications, Annals of Operations Research 90 (1999), pp. 45–63.</ref>

References

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External links

• wiktionary:eighty for 80 in other languages.