ANSWERS: 4
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When one player checks his opponent continously without a checkmate; no matter how his opponent moves. This kind of game usually ends in a draw if the same moves are repeated three times.
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Perpetual check involves continuosly checking your opponent until a draw occurs. The draw will occur when either 50 moves have occurred with no pawn move or no piece capture or due to threefold repetition. See http://en.wikipedia.org/wiki/Perpetual_check It is only perpetual check if it results in a draw. If you keep checking for up to 49 moves and then win or stop calling check then by definition it is no longer perpetual check.
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When you can check your opponent and then when he moves you can check him again without there being a way for your opponent to move so that you can't check him again in the next move.
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Perpetual check occurs when one player can--without interruption--continually put the other player into check. This will result in a draw either by threefold repetition, the 50-move rule, or agreement. The player bringing about the perpetual check is usually in a losing situation, and this is their last hope. Read more about perpetual check here: http://perpetualcheck.blogspot.com/2009/02/perpetual-check.html
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