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Given three jugs with x pints in the first, y in the second, and z in the third, obtain a desired amount in one of the vessels by completely filling up and/or emptying ...

In general, an arrangement of objects is simply a grouping of them. The number of "arrangements" of n items is given either by a combination (order is ignored) or permutation ...

A binary operation f(x,y) is an operation that applies to two quantities or expressions x and y. A binary operation on a nonempty set A is a map f:A×A->A such that 1. f is ...

The simplest dissection of a square into rectangles of the same areas but different shapes, composed of the seven pieces illustrated above. The square is 210 units on a side, ...

Two complex numbers z=x+iy and z^'=x^'+iy^' are added together componentwise, z+z^'=(x+x^')+i(y+y^'). In component form, (x,y)+(x^',y^')=(x+x^',y+y^') (Krantz 1999, p. 1).

Complex infinity is an infinite number in the complex plane whose complex argument is unknown or undefined. Complex infinity may be returned by the Wolfram Language, where it ...

The difference of two complex numbers z=x+iy and z^'=x^'+iy^' is given by z-z^'=(x-x^')+i(y-y^'). In component form, (x,y)-(x^',y^')=(x-x^',y-y^').

A compositeness certificate is a piece of information which guarantees that a given number p is composite. Possible certificates consist of a factor of a number (which, in ...

A number puzzle in which a group of arithmetical operations has some or all of its digits replaced by letters or symbols, and where the original digits must be found. In such ...

A diagonal of a square matrix which is traversed in the "southeast" direction. "The" diagonal (or "main diagonal," or "principal diagonal," or "leading diagonal") of an n×n ...