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For the last puzzle why not Rxb2, Re3+
... Re3+ then Kf2 and white can easily convert it in Philidor position which is theoretical draw.
Then the king will move back and it will be a draw by perpetual.
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Nice post !For people having trouble to understand what the stalemate rule exactly is, I suggest to have a look to the following blog post:chesstrainerapp.blogspot.com/2013/12/is-it-mate-or-stalemate-introduction.html