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A model mate is a type of pure mate checkmating position in chess in which not only is the checkmated king and all vacant squares in its field attacked only once, and squares in the king's field occupied by friendly units are not also attacked by the mating side (unless such a unit is necessarily pinned to the king), but all units of the mating side (with the possible exception of the king and pawns) participate actively in forming the mating net.
Model mates are extremely rare in practical play, but they add value to chess problems as they are considered artistic. In fact, they form the basis of the so-called Bohemian school of chess composition, most fruitful in threemovers and moremovers. Model mates are very usual in helpmates and they appear often in selfmates too.
The diagram on the left shows a problem by Miroslav Havel. The key 1. Bc5!! gives a flight square for the black King and threatens 2. Rxf6+ Ke4 3. Nf2# with a model mate. The main variations end with model mates from white batteries: 1... Kf4 2. Nxf6 (threat 3. Qg4#) 2... e4 3. Nd7#, and 1... Ke4 2. Nf2+ Kd5 3. Rc7#. There are several other variations (after 1... Ne4 and 1... Ke6), which do not end with model mates, and allow for multiple continuations. In the Bohemian school they are irrelevant, as long as they end with a mate in a prescribed number of moves.
The diagram on the right shows a helpmate, in which both sides cooperate to achieve a mate to the black king. It has two solutions ending in model mates (Black moves first in helpmates): 1. Re3 Ke6 2. Ke4 Rh4#, and 1. Kc5 Kc7 2. Rc4 Nc6# If all units of both colours are involved in a model mate, then it is an ideal mate. Both mates in the presented helpmate are ideal mates.