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Note 1: Using American Contract Bridge League (ACBL) methods, scoring is one point for each pair beaten, and one-half point for each pair tied. Note 2 : The rule of two matchpoints for each pair beaten is easy to apply in practice: if the board is played n times, the top result achieves 2 n −2 matchpoints, the next 2 n −4, down to zero.
The 4-3-2-1 high card point evaluation has been found to statistically undervalue aces and tens and alternatives have been devised to increase a hand's HCP value. To adjust for aces, Goren recommended [5] deducting one HCP for a hand without any aces and adding one for holding four aces. Some adjust for tens by adding 1/2 HCP for each. [1]
A simple arithmetic calculator was first included with Windows 1.0. [5]In Windows 3.0, a scientific mode was added, which included exponents and roots, logarithms, factorial-based functions, trigonometry (supports radian, degree and gradians angles), base conversions (2, 8, 10, 16), logic operations, statistical functions such as single variable statistics and linear regression.
where n > 1 is an integer and p, q, r are prime numbers, then 2 n × p × q and 2 n × r are a pair of amicable numbers. This formula gives the pairs (220, 284) for n = 2, (17296, 18416) for n = 4, and (9363584, 9437056) for n = 7, but no other such pairs are known. Numbers of the form 3 × 2 n − 1 are known as Thabit numbers.
A Langford pairing for n = 4. In combinatorial mathematics, a Langford pairing, also called a Langford sequence, is a permutation of the sequence of 2n numbers 1, 1, 2, 2, ..., n, n in which the two 1s are one unit apart, the two 2s are two units apart, and more generally the two copies of each number k are k units apart. Langford pairings are ...
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The closest pair of points problem or closest pair problem is a problem of computational geometry: given points in metric space, find a pair of points with the smallest distance between them. The closest pair problem for points in the Euclidean plane [ 1 ] was among the first geometric problems that were treated at the origins of the systematic ...
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