Pastimes: chess

Geometry overcomes force in this endgame study composed in 1976 by A Lewandowski. It is White to play and draw.

The most natural move to meet the threats of Bxe3+ or Nf3+ is 1.g4+ when 1...Nxg4 draws 2.Nxg4 Bxd6 3.Nf6+. So Black has to play 1...Kxh4 when we must check with the knight from g2 or f5.

2.Ng2+ loses to 2...Kg3 3.Nxf4 Nf3+ 4.Kf1 Rh1+ 5.Ke2 Re1+ 6.Kd3 Rd1+ followed by 7...Rxd6.

So it has to be 2.Nf5+ Kxg4, when the threat of Kxf5 or Nf3+ forces 3.Rf6, which loses to 3...Nd7. All of which means that 1.g4+ does not work at all. So what else?

Since the rook cannot defend the knight, and 1.Kf2 loses to 1...Bxe3+ 2.Kxe3 Nc4+, it has to be a knight move, and the only one that offers any promise is 1.Nd5, threatening Nxf4 or Nf6+.

After 1.Nd5 Nf3+ White must think again. 2.gxf3 is fine after 2...Bxd6, but Black flicks in 2...Rg7+ instead, and takes the rook next move.

So let's try 2.Kf2 when 2...Bxd6 3.Nf6+ wins back the rook. The trouble is that after 3...Kg6 4.Nxh7 Nxh4 the white knight is trapped and even 5.g3 Nf5 6.g4 Ng7 does not save it.

The solution is remarkable. It does indeed begin 1.Nd5 Nf3+ 2.gxf3! Rg7+ and now the extraordinary 3.Rg6!! Now 3...Kxg6 4.Nxf4+ Kf5 6.Ng2 draws easily, while 3...Rxg6+ 4.Kh1! sets up the final idea. Black must move his bishop to avoid its capture, when 5.Nf4+!! Bxf4 is stalemate.