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Sum and Product Puzzle. The Sum and Product Puzzle, also known as the Impossible Puzzle because it seems to lack sufficient information for a solution, is a logic puzzle. It was first published in 1969 by Hans Freudenthal, [1] [2] and the name Impossible Puzzle was coined by Martin Gardner. [3] The puzzle is solvable, though not easily.
The sum of four cubes problem [1] asks whether every integer is the sum of four cubes of integers. It is conjectured the answer is affirmative, but this conjecture has been neither proven nor disproven. [2] Some of the cubes may be negative numbers, in contrast to Waring's problem on sums of cubes, where they are required to be positive.
A facility location problem is the problem of deciding where a given public facility (e.g. a school or a power station) should be placed. This problem has been studied from various angles. Optimal facility location is an optimization problem: deciding where to place the facility in order to minimize transportation costs while considering ...
The divisor summatory function is defined as. where. is the divisor function. The divisor function counts the number of ways that the integer n can be written as a product of two integers. More generally, one defines. where dk ( n) counts the number of ways that n can be written as a product of k numbers. This quantity can be visualized as the ...
Generalization of Diophantus's solution. Diophantus II.VIII: Generalized solution in which the sides of triangle OAB form a rational triple if line CB has a rational gradient t. We may generalize Diophantus's solution to solve the problem for any given square, which we will represent algebraically as a2. Also, since Diophantus refers to an ...
The connected sum is a local operation on manifolds, meaning that it alters the summands only in a neighborhood of . This implies, for example, that the sum can be carried out on a single manifold containing two disjoint copies of , with the effect of gluing to itself. For example, the connected sum of a 2-sphere at two distinct points of the ...
In computer science, sorting is the problem of sorting pairs of numbers by their sums. Applications of the problem include transit fare minimisation, VLSI design, and sparse polynomial multiplication. As with comparison sorting and integer sorting more generally, algorithms for this problem can be based only on comparisons of these sums, or on ...
The 3-partition problem is similar to the partition problem, in which the goal is to partition S into two subsets with equal sum, and the multiway number partitioning, in which the goal is to partition S into k subsets with equal sum, where k is a fixed parameter. In 3-Partition the goal is to partition S into m = n /3 subsets, not just a fixed ...