Both today's positions are endgame studies by the Ukrainian composer Ernest Pogosyants, and both display remarkable richness of play for the minimalist amount of material used. Both are White to play and win.

In the first, since 1.d6? is met by 1...Nf5+, the start is easy enough: 1.Kf6 Kh6 2.d6. Now 2...Nh5+ 3.Kf7 leaves Black unable to stop the pawn marching home. But he has a clever idea instead: 2...Ne8+! 3.Bxe8 e3. If White tries to stop the pawn with 4.Bb5, then Black saves himself by stalemate after 4...e2! 5.Bxe2.

So White must push on with 4.d7 e2, but after 5.d8=Q e1=Q White has no good check. There is not even any good way to try to win. We have to go back a move. Instead of 5.d8=Q, try promoting to a knight! After 5.d8=N! e1=Q, White plays 6.Nf7+ Kh5 7.Ne5+ when 7...Kh6 8.Ng4 is mate, while 7...Kh4 8.Nf3+ wins the queen.

Very clever, but that's only half of the answer. Suppose Black meets 5.d8=N! with 5...e1=N! Then 6.Nf7+ Kh5 7.Ne5+ Kh4 leads to nothing for White. Instead, White plays the subtle 6.Nc6! Nf3 (or Nd3) 7.Ne7 Nh4 (to stop Nf5 mate) 8.Ng8 mate.

The second position reaches a similar end through very different means. A pawn behind and facing the threat of 1...Qg7 mate, White needs to create a heavy threat himself and the way to do it is 1.Qf7 (note that 1.Qc7 would allow Be6+) threatening both Qh7 mate and Qh5 mate. Now see if you can find Black's ingenious defence. It looks as though he is helpless, but there is a splendid resource: 1...Qh8+! 2.Kxh8 a1=Q+ 3.Kg8 Qh8+! 4.Kxh8 Ng6+ 5.Kg8 Be6! Finally the point is clear: 6.Qxe6 is stalemate. But White plays instead 6.Ng5! Bxf7+ 7.Nxf7 mate! Note that 6...Ne7+ 7.Kf8 Ng6+ would have lost to 8.Qxg6+ Kxg6 9.Nxe6, but this defence works after 6.Nd6?