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Find nontrivial solutions to sigma(x^2)=sigma(y^2) other than (x,y)=(4,5), where sigma(n) is the divisor function. Nontrivial solutions means that solutions which are ...

The determination of the number of alternating permutations having elements {1,2,...,n}.

Cut a sphere by a plane in such a way that the volumes of the spherical segments have a given ratio.

In a given acute triangle DeltaABC, locate a point whose distances from A, B, and C have the smallest possible sum. The solution is the point from which each side subtends an ...

The rook is a chess piece that may move any number of spaces either horizontally or vertically per move. The maximum number of nonattacking rooks that may be placed on an n×n ...

Consider the probability Q_1(n,d) that no two people out of a group of n will have matching birthdays out of d equally possible birthdays. Start with an arbitrary person's ...

Given a group of n men arranged in a circle under the edict that every mth man will be executed going around the circle until only one remains, find the position L(n,m) in ...

In the early 1950s, Ernst Straus asked 1. Is every region illuminable from every point in the region? 2. Is every region illuminable from at least one point in the region? ...

Sangaku problems, often written "san gaku," are geometric problems of the type found on devotional mathematical wooden tablets ("sangaku") which were hung under the roofs of ...

Let n objects be picked repeatedly with probability p_i that object i is picked on a given try, with sum_(i)p_i=1. Find the earliest time at which all n objects have been ...