economical flights

In chess, an economical mate is a checkmate position such that all of the attacker's remaining knights, bishops, rooks and queens contribute to the mating attack. The attacker's king and pawns may also contribute to the mate, but their assistance is not required, nor does it disqualify the position from being an economical mate. Economical mates are of interest to chess problem composers for their aesthetic value. In real gameplay, their occurrence is incidental. Nevertheless, some notable games have concluded with an economical mate such as the Opera game, won by Paul Morphy.
In chess problem composition, the concept of an economical mate is motivated by the aesthetic notion of economy of force, the idea that a composition is simpler and more beautiful when it uses minimal material to maximal effect. When all of the attacker's pieces—apart from the king and pawns—contribute to a checkmate, this also means that none of the more powerful units have been left unused, an economical use of material.
Economical mate is one of a few terms used by composers to describe the properties of checkmate positions; related concepts include pure mate, model mate, and ideal mate. A pure mate is a position such that the mated king is attacked once and prevented from moving to any of the adjacent squares in its field for exactly one reason per square. Model mate and ideal mate are both stronger forms of pure mate. When a checkmate is both "pure and economical", it is said to be a model mate. When, in a pure mate, all material on the board of either color plays a direct role in the checkmate, it is said to be an ideal mate.

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