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Link doesn't work.

It is 50 moves with no captures or pawn moves. Your opponent had a pawn (and was moving it) through move 84 so you never met the 50 move condition after that. Before that, there were plenty of captures and pawn moves that the condition wasn't met before that either. A capture or pawn move resets the count.

I presume the game in question is this one: http://www.chess.com/livechess/game.html?id=145250257

You don't have a case as the last pawn move was made on move 84 so you could only claim a draw at move 134. Let's review the rule: You can claim a draw if 50 moves have been made and no piece has been taken and no pawn moves have been made. I am sensing that you thought that your opponent needs to checkmate you in 50 moves which is incorrect.

AumTerre, It is interesting that your opponent in move 84 promoted his pawn to a rook instead of a queen. He then played only with the king and rook and left the knight behind. Maybe he wanted to practise his skills in making a mate with just the rook and king, who knows? It took him 27 moves, so there is a long way up to 50 moves as others have already pointed out. Anyway in move 84 there is actually a mate in 3 and that would have been a lot simpler to perform. Here it is as a puzzle just for the fun of it:

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Actually, there were pawn moves at 65, 69, 70, 83 and 84 ... So even with the first one you would have needed to hang on for another four moves ..