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In a boarding school there are fifteen schoolgirls who always take their daily walks in rows of threes. How can it be arranged so that each schoolgirl walks in the same row ...

A group of five elements.

A group of five elements, also called a quintuplet or pentad.

Three sets of three lines such that each line is incident with two from both other sets.

A set of four, also called a quartet.

A puzzle in which one object is to be converted to another by making a finite number of cuts and reassembling it. The cuts are often, but not always, restricted to straight ...

The geometric mean of a sequence {a_i}_(i=1)^n is defined by G(a_1,...,a_n)=(product_(i=1)^na_i)^(1/n). (1) Thus, G(a_1,a_2) = sqrt(a_1a_2) (2) G(a_1,a_2,a_3) = ...

The harmonic mean H(x_1,...,x_n) of n numbers x_i (where i=1, ..., n) is the number H defined by 1/H=1/nsum_(i=1)^n1/(x_i). (1) The harmonic mean of a list of numbers may be ...

The vector triple product identity Ax(BxC)=B(A·C)-C(A·B). This identity can be generalized to n dimensions,

The algebraic identity (sum_(i=1)^na_ic_i)(sum_(i=1)^nb_id_i)-(sum_(i=1)^na_id_i)(sum_(i=1)^nb_ic_i) =sum_(1<=i<j<=n)(a_ib_j-a_jb_i)(c_id_j-c_jd_i). (1) Letting c_i=a_i and ...