What is "magic number"

n. 1 (context physics English) the number of neutrons or protons in nuclei which are required to fill the major quantum shells, and thus produce exceptionally stable nuclei - 2, 8, 20, 28, 50, 82 & 126 2 (context baseball English) A metric used to determine a team's required performance to make the playoffs. 3 # The sum of one and the wins by one team and losses by an opponent necessary for the team to ensure the opponent cannot catch it in the standings by the end of the regular season. In Major League Baseball, with a regular season of 162 games, the magic number '''M''' is calculated as '''M = 163 - W₁ - L₂''', in which W₁ is the leading team's current win total, and L₂ is the opponent's current loss total. A magic number of 0 indicates that the trailing team cannot catch the leading team. 4 # By extension, the lowest such number that assures a team a playoff berth. 5 (context computing English) 6 # a number which is manually entered into source code, rather than defined somewhere as a named constant; especially one which is arbitrary or lacks explanation. 7 # a number which cannot occur in normal use, typically used as a placeholder (e.g. a fictitious date such as 2000-02-32). 8 # a hash code, such as those used by some webmail servers to keep track of sessions.

n. the atomic number of an extra stable strongly bound atomic nucleus: 2, 8, 20, 28, 50, 82 or 126

Magic number may refer to:

• Magic number (chemistry), number of atoms or molecules forming an exceptionally stable cluster
• Magic number (sports), a number that indicates how close a team is to winning a season title
• Magic number (oil), the price per barrel of oil at which an oil exporting nation runs a deficit
• Magic number (physics), the number of nucleons that results in complete atomic-nuclear shells
• Magic number (programming), originally the UNIX way of recognizing file types. Can also mean unique literals with unexplained meaning or multiple occurrences in code which could (preferably) be replaced with named constants.
• Magic Numbers (TV series)
• Magic Number (game), a pricing game on The Price is Right
• "Magic Number" (Maaya Sakamoto song)
• " The Magic Number", a 1990 song by De La Soul from 3 Feet High and Rising
• The Magic Numbers, a British rock band

In nuclear physics, a magic number is a number of nucleons (either protons or neutrons) such that they are arranged into complete shells within the atomic nucleus. The seven most widely recognized magic numbers as of 2007 are 2, 8, 20, 28, 50, 82, and 126 . Atomic nuclei consisting of such a magic number of nucleons have a higher average binding energy per nucleon than one would expect based upon predictions such as the semi-empirical mass formula and are hence more stable against nuclear decay.

The unusual stability of isotopes having magic numbers means that transuranium elements can be created with extremely large nuclei and yet not be subject to the extremely rapid radioactive decay normally associated with high atomic numbers. Large isotopes with magic numbers of nucleons are said to exist in an island of stability. Unlike the magic numbers 2–126, which are realized in spherical nuclei, theoretical calculations predict that nuclei in the island of stability are deformed. Before this was realized, higher magic numbers, such as 184, 258, 350, and 462 , were predicted based on simple calculations that assumed spherical shapes: these are generated by the formula $2(\tbinom n1+ \tbinom n2+\tbinom n3)$ (see binomial coefficient). It is now believed that the sequence of spherical magic numbers cannot be extended in this way. Further predicted magic numbers are 114, 122, 124, and 164 for protons as well as 184, 196, 236, and 318 for neutrons.

The magic number is a term in economics that denotes the price of crude oil (measured in dollars per barrel) at which a crude oil exporting economy runs a deficit.

Some countries support almost all spending from income derived from oil exports. As the price of oil drops, these countries take in less revenue from oil. The magic number denotes the point at which the revenue from oil is no longer sufficient to pay for spending. Mathematically, this can be expressed by the inequality:

Q × P > S

where Q is the quantity of oil exported, P is the price, and S is spending. The magic number is the value of P at which this inequality no longer holds true - that is, that the economy runs a deficit.

PFC Energy publishes the magic number for all the OPEC nations.

" Qatar is at $21 a barrel, because it brings in much more oil money than it spends. Saudi Arabia's break-even point is at $49 a barrel. And Venezuela is at $58, second only to Nigeria's $65."

is Maaya Sakamoto's eighteenth single. The title track was used as the opening theme for the anime Kobato. The live version of Kazamidori and Pocket wo Kara ni Shite are from her concert at Tokyo International Forum Hall A on January 24, 2009 with live arrangement by Shin Kōno.

In certain sports, a magic number is a number used to indicate how close a front-running team is to clinching a division title and/or a playoff spot. It represents the total of additional wins by the front-running team or additional losses (or any combination thereof) by the rival team after which it is mathematically impossible for the rival team to capture the title in the remaining games. This assumes that each game results in a win or a loss, but not a tie. Teams other than the front-running team have what is called an elimination number (or "tragic number") (often abbreviated E#). This number represents the number of wins by the leading team or losses by the trailing team which will eliminate the trailing team. The elimination number for the second place team is exactly the magic number for the leading team.

The magic number is calculated as G + 1 − W − L, where

• G is the total number of games in the season
• W is the number of wins that Team A has in the season
• L is the number of losses that Team B has in the season

For example, in Major League Baseball there are 162 games in a season. Suppose the top of the division standings late in the season are as follows:

Team

Wins

Losses

A

96

58

B

93

62

Then the magic number for Team A to win the division is 162 + 1 − 96 − 62 = 5.

Any combination of wins by Team A and losses by Team B totaling to 5 makes it impossible for Team B to win the division title.

The "+1" in the formula serves the purpose of eliminating ties; without it, if the magic number were to decrease to zero and stay there, the two teams in question would wind up with identical records. If circumstances dictate that the front-running team would win the tiebreaker regardless of any future results, then the additional constant 1 can be eliminated. For example, the NBA uses complicated formulae for breaking ties, using several other statistics of merit besides overall win/loss record; however the first tiebreaker between two teams is their head-to-head record; if the frontrunning team has already clinched the better head-to-head record, then the +1 is unnecessary.

The magic number can also be calculated as W + GR - W + 1, where

• W is the number of wins that Team B has in the season
• GR is the number of games remaining for Team B in the season
• W is the number of wins that Team A has in the season

This second formula basically says: Assume Team B wins every remaining game. Calculate how many games team A needs to win to surpass team B's maximum total by 1. Using the example above and with the same 162-game season, team B has 7 games remaining.

The magic number for Team A to win the division is still "5": 93 + 7 − 96 + 1 = 5.

Team B can win as many as 100 games. If Team A wins 101, Team B is eliminated. The magic number would decrease with a Team A win and would also decrease with a Team B loss, as its maximum win total would decrease by one.

A variation of the above looks at the relation between the losses of the two teams. The magic number can be calculated as L + GR - L + 1, where

• L is the number of losses that Team A has in the season
• GR is the number of games remaining for Team A in the season
• L is the number of losses that Team B has in the season

This third formula basically says: Assume Team A loses every remaining game. Calculate how many games team B needs to lose to surpass team A's maximum total by 1. Using the example above and with the same 162-game season, team A has 8 games remaining.

The magic number for Team A to win the division is still "5": 58 + 8 − 62 + 1 = 5. As you can see, the magic number is the same whether calculating it based on potential wins of the leader or potential losses of the trailing team. Indeed, mathematical proofs will show that the three formulas presented here are mathematically equivalent.

Team A can lose as many as 66 games. If Team B loses 67, Team B is eliminated. Once again, the magic number would decrease with a Team A win and would also decrease with a Team B loss.

In some sports, ties are broken by an additional one-game playoff(s) between the teams involved. When a team gets to the point where its magic number is 1, it is said to have "clinched a tie" for the division or the wild card. However, if they end the season tied with another team, and only one is eligible for the playoffs, the extra playoff game will erase that "clinching" for the team that loses the playoff game.

By convention, the magic number typically is used to describe the first place team only, relative to the teams it leads. However, the same mathematical formulas could be applied to any team, teams that are tied for the lead, as well as teams that trail. In these cases, a team that is not in first place will depend on the leading team to lose some games so that it may catch up, so the magic number will be larger than the number of games remaining. Ultimately, for teams that are no longer in contention, their magic number would be larger than their remaining games + the remaining games for the first place team — which would be impossible to overcome.

In computer programming, the term magic number has multiple meanings. It could refer to one or more of the following:

• A constant numerical or text value used to identify a file format or protocol; for files, see List of file signatures
• Distinctive unique values that are unlikely to be mistaken for other meanings (e.g., Globally Unique Identifiers)
• Unique values with unexplained meaning or multiple occurrences which could (preferably) be replaced with named constants

The concept of magic numbers refer to a specific properties (such as stability) for only certain representatives among a distribution of species.

The concept of magic numbers (in the field of chemistry) was first recognized by inspecting the intensity of mass-spectrometric signals of rare gas cluster ions. In case a gas condenses into clusters of atoms, the number of atoms in these clusters, that form most likely, varies between a few and hundreds. However, there are peaks at specific cluster sizes, deviating from a pure statistical distribution. Therefore, it was concluded that clusters of these specific numbers of rare gas atoms dominate due to their exceptional stability. The concept was also successfully applied to explain the monodispersed occurrence of thiolate-protected gold clusters; here the outstanding stability of specific cluster sizes is connected with their respective electronic configuration.

The term magic numbers, is used also in the field of nuclear physics. In this context, magic numbers often represent three-dimensional figurate numbers such as the octahedral numbers: they count the numbers of spheres in sphere packings of Platonic solids and related polyhedra.