80 (number)

In mathematics

80 is:

• The sum of Euler's totient function φ(x) over the first sixteen integers: : 1 + 1 + 2 + 2 + 4 + 2 + 6 + 4 + 6 + 4 + 10 + 4 + 12 + 6 + 8 + 8 = 80.
• A semiperfect number, since adding up some subsets of its divisors (e.g., 1, 4, 5, 10, 20, and 40) gives 80.
• A ménage number.
• 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 four twin prime pairs: : (3 + 5) + (5 + 7) + (11 + 13) + (17 + 19) = 80.

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 15 puzzle can be solved in no more than 80 single-tile moves.

References

References

1. "Sloane's A005835: Pseudoperfect (or semiperfect) numbers". OEIS Foundation.
2. "Sloane's A000179: Ménage numbers". OEIS Foundation.
3. Bunkley, Nick. (March 3, 2008). "Joseph Juran, 103, Pioneer in Quality Control, Dies". [[The New York Times]].
4. "What is 80/20 Rule, Pareto's Law, Pareto Principle".
5. A. Brüngger, A. Marzetta, K. Fukuda, and J. Nievergelt, [https://www.iro.umontreal.ca/~gendron/Pisa/References/BB/Brungger99.pdf The parallel search bench ZRAM and its applications], ''Annals of Operations Research'' '''90''' (1999), pp. 45–63.