My advanced class drew one card from each of three packets: pawn ending cards, rook endings, middlegame positions (from GM-RAM). The first two are from Dvoretsky's Endgame Manual. We labored together to find the solutions with mixed success.
Black to move
Most of the students were convinced that White was winning the pawn ending. I played Black and slowly convinced the students of the truth of the position.
White to move/Black to move
The rook ending position is two positions--White to move and Black to move. We only looked at White. The students tried several schemes that failed, but with correct play, White can transfer the move to Black. Then, it becomes clear that Black is in zugzwang.
White to move
This position arose in Morphy -- De Riviere, Paris 1863. The students favored Morphy's move (18.g4), which may not be best. However, they struggled with my refutation (18...Rh7). De Riviere played 18...Rxh3, which is superior to 18...Rh7. The group saw 19.Bxf6 Nxf6, but not 20.Ng5!