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The longest path problem asks to find a path of maximum length in a given graph. The problem is NP-complete, but there exists an efficient dynamic programming solution for ...

Twenty golfers wish to play in foursomes for 5 days. Is it possible for each golfer to play no more than once with any other golfer? The answer is yes, and the following ...

Given a ship with a known constant direction and speed v, what course should be taken by a chase ship in pursuit (traveling at speed V) in order to intercept the other ship ...

Archimedes' cattle problem, also called the bovinum problema, or Archimedes' reverse, is stated as follows: "The sun god had a herd of cattle consisting of bulls and cows, ...

A well-known nursery rhyme states, "As I was going to St. Ives, I met a man with seven wives. Every wife had seven sacks, every sack had seven cats, every cat had seven ...

A related rates problem is the determination of the rate at which a function defined in terms of other functions changes. Related rates problems can be solved by computing ...

The rational distance problem asks to find a geometric configuration satisfying given properties such that all distances along specific edges are rational numbers. (This is ...

In 1657, Fermat posed the problem of finding solutions to sigma(x^3)=y^2, and solutions to sigma(x^2)=y^3, where sigma(n) is the divisor function (Dickson 2005). The first ...

A maximum clique of a graph G is a clique (i.e., complete subgraph) of maximum possible size for G. Note that some authors refer to maximum cliques simply as "cliques." The ...

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 ...