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The smallest (and unique up to rotation and reflection) non-trivial case of a magic square, order 3. In mathematics, especially historical and recreational mathematics, a square array of numbers, usually positive integers, is called a magic square if the sums of the numbers in each row, each column, and both main diagonals are the same.
The number of possible positions of the 24 puzzle is 25! / 2 ≈ 7.76 × 10 24, which is too many to calculate God's number feasibly using brute-force methods. In 2011, lower bounds of 152 single-tile moves or 41 multi-tile moves had been established, as well as upper bounds of 208 single-tile moves or 109 multi-tile moves.
Dih n: the dihedral group of order 2n (often the notation D n or D 2n is used) K 4: the Klein four-group of order 4, same as Z 2 × Z 2 and Dih 2; D 2n: the dihedral group of order 2n, the same as Dih n (notation used in section List of small non-abelian groups) S n: the symmetric group of degree n, containing the n! permutations of n elements
Sociable numbers are the numbers in cyclic lists of numbers (with a length greater than 2) where each number is the sum of the proper divisors of the preceding number. For example, 1264460 ↦ 1547860 ↦ 1727636 ↦ 1305184 ↦ 1264460 ↦ … {\displaystyle 1264460\mapsto 1547860\mapsto 1727636\mapsto 1305184\mapsto 1264460\mapsto \dots } are ...
Andersson et al. (1998) provide a randomized algorithm called signature sort that allows for linear time sorting of sets of up to 2 O((log w) 1/2 − ε) items at a time, for any constant ε > 0. As in the algorithm of Kirkpatrick and Reisch, they perform range reduction using a representation of the keys as numbers in base b for a careful ...
In mathematics and computer science, the sorting numbers are a sequence of numbers introduced in 1950 by Hugo Steinhaus for the analysis of comparison sort algorithms. These numbers give the worst-case number of comparisons used by both binary insertion sort and merge sort. However, there are other algorithms that use fewer comparisons.
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