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1/52! chance of a specific shuffle Mathematics: The chances of shuffling a standard 52-card deck in any specific order is around 1.24 × 10 −68 (or exactly 1 ⁄ 52!) [4] Computing: The number 1.4 × 10 −45 is approximately equal to the smallest positive non-zero value that can be represented by a single-precision IEEE floating-point value.
There is also a triangular array associated with the Schröder numbers that provides a recurrence relation [6] (though not just with the Schröder numbers). The first few terms are 1, 1, 2, 1, 4, 6, 1, 6, 16, 22, .... (sequence A033877 in the OEIS). It is easier to see the connection with the Schröder numbers when the sequence is in its ...
A line graph has an articulation point if and only if the underlying graph has a bridge for which neither endpoint has degree one. [2] For a graph G with n vertices and m edges, the number of vertices of the line graph L(G) is m, and the number of edges of L(G) is half the sum of the squares of the degrees of the vertices in G, minus m. [6]
In 493 AD, Victorius of Aquitaine wrote a 98-column multiplication table which gave (in Roman numerals) the product of every number from 2 to 50 times and the rows were "a list of numbers starting with one thousand, descending by hundreds to one hundred, then descending by tens to ten, then by ones to one, and then the fractions down to 1/144."
1 in 1 744 278: Every 4776 years (once in recorded history) μ ± 5.5σ: 0.999 999 962 020 875: 3.798 × 10 −8 = 37.98 ppb: 1 in 26 330 254: Every 72 090 years (thrice in history of modern humankind) μ ± 6σ: 0.999 999 998 026 825: 1.973 × 10 −9 = 1.973 ppb: 1 in 506 797 346: Every 1.38 million years (twice in history of humankind) μ ± ...
Counting the number of unlabeled free trees is a harder problem. No closed formula for the number t(n) of trees with n vertices up to graph isomorphism is known. The first few values of t(n) are 1, 1, 1, 1, 2, 3, 6, 11, 23, 47, 106, 235, 551, 1301, 3159, … (sequence A000055 in the OEIS). Otter (1948) proved the asymptotic estimate
/// Performs a Karatsuba square root on a `u64`. pub fn u64_isqrt (mut n: u64)-> u64 {if n <= u32:: MAX as u64 {// If `n` fits in a `u32`, let the `u32` function handle it. return u32_isqrt (n as u32) as u64;} else {// The normalization shift satisfies the Karatsuba square root // algorithm precondition "a₃ ≥ b/4" where a₃ is the most ...
1. Men and women of full age, without any limitation due to race, nationality or religion, have the right to marry and to found a family. They are entitled to equal rights as to marriage, during marriage and at its dissolution. 2. Marriage shall be entered into only with the free and full consent of the intending spouses. 3.