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SOLUTION

PUZZLE #1

White: 3 pieces (Kc4, We3, Ri4)
Black: 2 pieces (Ka4, Pb4)
White to move and mate in two.

After the key-move, 1.Wb2, black's only move is Pb3, cutting off blacks potential flight square at b3, whereupon 2.Kc5 unleashes an ambush from the White Rook.