Search Results for ""

Find two distinct sets of integers {a_1,...,a_n} and {b_1,...,b_n}, such that for k=1, ..., m, sum_(i=1)^na_i^k=sum_(i=1)^nb_i^k. (1) The Prouhet-Tarry-Escott problem is ...

1. Find a complete system of invariants, or 2. Decide when two metrics differ only by a coordinate transformation. The most common statement of the problem is, "Given metrics ...

The complementary subspace problem asks, in general, which closed subspaces of a Banach space are complemented (Johnson and Lindenstrauss 2001). Phillips (1940) proved that ...

Also called the ménage problem. In how many ways can n married couples be seated around a circular table in such a manner than there is always one man between two women and ...

Find the shape of a soap film (i.e., minimal surface) which will fill two inverted conical funnels facing each other is known as Sinclair's soap film problem (Bliss 1925, p. ...

Let X be an arbitrary topological space. Denote the set closure of a subset A of X by A^- and the complement of A by A^'. Then at most 14 different sets can be derived from A ...

Sylvester's four-point problem asks for the probability q(R) that four points chosen at random in a planar region R have a convex hull which is a quadrilateral (Sylvester ...

The Buffon-Laplace needle problem asks to find the probability P(l,a,b) that a needle of length l will land on at least one line, given a floor with a grid of equally spaced ...

Is it possible to cover completely the surface of a sphere with congruent, nonoverlapping arcs of great circles? Conway and Croft (1964) proved that it can be covered with ...

An unsolved problem in mathematics attributed to Lehmer (1933) that concerns the minimum Mahler measure M_1(P) for a univariate polynomial P(x) that is not a product of ...