Puzzle for my students

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In this game, Black (me) has blundered a whole rook but still has 2 connected passed wing pawns.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Find 2 or 3 candidate moves for Black and justify your plan for each.

 

 

 

 

Rc1+ was the moved played. How would you defend as White? Justify your plan with careful analysis.