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Given three objects, each of which may be a point, line, or circle, draw a circle that is tangent to each. There are a total of ten cases. The two easiest involve three ...

The determination of whether a Turing machine will come to a halt given a particular input program. The halting problem is solvable for machines with less than four states. ...

If f(x,y) is an analytic function in a neighborhood of the point (x_0,y_0) (i.e., it can be expanded in a series of nonnegative integer powers of (x-x_0) and (y-y_0)), find a ...

The problem of determining the vertices of a Schwarz-Christoffel mapping (Krantz 1999, p. 176).

Brocard's problem asks to find the values of n for which n!+1 is a square number m^2, where n! is the factorial (Brocard 1876, 1885). The only known solutions are n=4, 5, and ...

The goat problem (or bull-tethering problem) considers a fenced circular field of radius a with a goat (or bull, or other animal) tied to a point on the interior or exterior ...

The problem of finding the number of different ways in which a product of n different ordered factors can be calculated by pairs (i.e., the number of binary bracketings of n ...

The traveling salesman problem is a problem in graph theory requiring the most efficient (i.e., least total distance) Hamiltonian cycle a salesman can take through each of n ...

Let there be m doctors and n<=m patients, and let all mn possible combinations of examinations of patients by doctors take place. Then what is the minimum number of surgical ...

Draw a circle that cuts three given circles perpendicularly. The solution is known as the radical circle of the given three circles. If it lies outside the three circles, ...