Search results
Results from the WOW.Com Content Network
2. 1. Crazy dice is a mathematical exercise in elementary combinatorics, involving a re-labeling of the faces of a pair of six-sided dice to reproduce the same frequency of sums as the standard labeling. The Sicherman dice are crazy dice that are re-labeled with only positive integers. (If the integers need not be positive, to get the same ...
The partial sums of the series 1 + 2 + 3 + 4 + 5 + 6 + ⋯ are 1, 3, 6, 10, 15, etc.The nth partial sum is given by a simple formula: = = (+). This equation was known ...
A Pythagorean triple consists of three positive integers a, b, and c, such that a2 + b2 = c2. Such a triple is commonly written (a, b, c), a well-known example is (3, 4, 5). If (a, b, c) is a Pythagorean triple, then so is (ka, kb, kc) for any positive integer k. A triangle whose side lengths are a Pythagorean triple is a right triangle and ...
The idea becomes clearer by considering the general series 1 − 2x + 3x 2 − 4x 3 + 5x 4 − 6x 5 + &c. that arises while expanding the expression 1 ⁄ (1+x) 2, which this series is indeed equal to after we set x = 1.
For instance, 6 has proper divisors 1, 2 and 3, and 1 + 2 + 3 = 6, so 6 is a perfect number. The next perfect number is 28, since 1 + 2 + 4 + 7 + 14 = 28. The first four perfect numbers are 6, 28, 496 and 8128. [1] The sum of proper divisors of a number is called its aliquot sum, so a perfect number is one that is equal to its aliquot sum.
A. 2 + 6 + 6 = 14 B. 3 + 3 + 8 = 14. In case 'A', there is no 'eldest child': two children are aged six (although one could be a few minutes or around 9 to 12 months older and they still both be 6). Therefore, when told that one child is the eldest, the census-taker concludes that the correct solution is 'B'. [3]
The values of a[2] and a[3] are swapped to form the new sequence [1, 2, 4, 3]. The sequence after k-index a[2] to the final element is reversed. Because only one value lies after this index (the 3), the sequence remains unchanged in this instance. Thus the lexicographic successor of the initial state is permuted: [1, 2, 4, 3].
An early example of answer set programming was the planning method proposed in 1997 by Dimopoulos, Nebel and Köhler. [3] [4] Their approach is based on the relationship between plans and stable models. [5] In 1998 Soininen and Niemelä [6] applied what is now known as answer set programming to the problem of product configuration. [4]