Chess

This year is the centenary of the first publication of one of the most remarkable endgame studies ever seen. For the above diagram first appeared in the Russian magazine Novoye Vremya in 1897.

Its composer, Alexei Troitsky, published around 800 problems and studies in a career that lasted from 1893 until his death in 1942. He also established the conditions under which king and two knights can win against king and pawn.

If you have not seen the diagram position before, the solution is guaranteed to astound. It is White to play and win.

White seems at first sight to be doing well enough with his extra queen, but then you notice that the threats of 1...Rb1+ and 1...g2 are not easy to meet. 1.Qf1+ g2 only makes matters worse, and the rook on b4 infuriatingly stops both Nf4+ and Qb7.

Now watch the answer: 1.Bc6! Rb1+ 2.Ke2 Rxh1 3.Bg2+!! Kxg2 4.Nf4+ Kg1 and now the splendid finale: 5.Ke1! Black must advance his pawn to g2 - he has no other move - and then 6.Ne2 is mate.

Here is another Troitsky puzzle, less startling, but just as elegant. It is White to play and draw. The black f-pawn is unstoppable, but here's how to deal with it: 1.Bb4+ Kb3 (Kxb4 allows Nd3+) 2.Nf3! f1=Q+ 3.Be1 Qg2 (Qxe2 loses to Nd4+) 4.Bg3! Kc3 5.Kd1 Qh1+ 6.Be1+ Kc4 7.Kd2 Qg2 8.Bg3! and the queen never gets out.