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80 (number)
80 (eighty) is the natural number following 79 and preceding 81. == In mathematics ==
The sum of Euler's totient function φ(''x'') over the first sixteen integers is 80. Adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20 and 40) gives 80, hence 80 is a semiperfect number. 80 is a ménage number, and is a Harshad number in base 10. 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.〔.〕〔.〕 Every solvable configuration of the Fifteen puzzle can be solved in no more than 80 single-tile moves.〔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.〕
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