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Let one grain of wheat be placed on the first square of a chessboard, two on the second, four on the third, eight on the fourth, etc. How many grains total are placed on an ...

The circumcenter of mass is a concept that can be defined by analogy with one of the the constructions for the geometric centroid for the case of polygons. The geometric ...

Fisher's exact test is a statistical test used to determine if there are nonrandom associations between two categorical variables. Let there exist two such variables X and Y, ...

The circumcircle of the Fuhrmann triangle. It has the line HNa, where H is the orthocenter and Na is the Nagel point, as its diameter. In fact, these points (Kimberling ...

In a rectangular room (a cuboid) with dimensions 30^'×12^'×12^', a spider is located in the middle of one 12^'×12^' wall one foot away from the ceiling. A fly is in the ...

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 ...

Elder's theorem is a generalization of Stanley's theorem which states that the total number of occurrences of an integer k among all unordered partitions of n is equal to the ...

A k×n Latin rectangle is a k×n matrix with elements a_(ij) in {1,2,...,n} such that entries in each row and column are distinct. If k=n, the special case of a Latin square ...

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 ...

The total number of contravariant and covariant indices of a tensor. The rank R of a tensor is independent of the number of dimensions N of the underlying space. An intuitive ...