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A sequence of numbers alpha_n is said to be uncorrelated if it satisfies lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_m^2=1 lim_(n->infty)1/(2n)sum_(m=-n)^nalpha_malpha_(k+m)=0 for ...

Let two players each have a finite number of pennies (say, n_1 for player one and n_2 for player two). Now, flip one of the pennies (from either player), with each player ...

A sultan has granted a commoner a chance to marry one of his n daughters. The commoner will be presented with the daughters one at a time and, when each daughter is ...

Bridge is a card game played with a normal deck of 52 cards. The number of possible distinct 13-card hands is N=(52; 13)=635013559600, (1) where (n; k) is a binomial ...

Poker is a card game played with a normal deck of 52 cards. Sometimes, additional cards called "jokers" are also used. In straight or draw poker, each player is normally ...

A flow defined analogously to the Anosov diffeomorphism, except that instead of splitting the tangent bundle into two invariant sub-bundles, they are split into three (one ...

Consider the excircles J_A, J_B, and J_C of a triangle, and the external Apollonius circle Gamma tangent externally to all three. Denote the contact point of Gamma and J_A by ...

A factorization of the form 2^(4n+2)+1=(2^(2n+1)-2^(n+1)+1)(2^(2n+1)+2^(n+1)+1). (1) The factorization for n=14 was discovered by Aurifeuille, and the general form was ...

A k-automatic set is a set of integers whose base-k representations form a regular language, i.e., a language accepted by a finite automaton or state machine. If bases a and ...

Given a complex Hilbert space H with associated space L(H) of continuous linear operators from H to itself, the bicommutant M^('') of an arbitrary subset M subset= L(H) is ...