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I have only king left with two pawns but they are blocked. By how many moves an opponent has to checkmate me?

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There is no such limit. In the official rules, §9.3, it is stated that there's a limit of 50 moves during which a pawn must move or a piece/pawn must be captured. If that doesn't happen, you can claim a draw.

I have heard that there are some circles a stronger limit is imposed when the weaker side has only a lone king (so, not two pawns), but those are unofficial rules and we can't say much about that.

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