Part of the charm and the allure of chess is that sometimes the seemingly impossible can be achieved. Understandably, this phenomenon is more prevalent in the realm of chess problems where the composers take great delight in tasking us with discovering solutions that seem both illogical and irrational. Here’s an old chestnut from the mind of the wily T.R. Dawson to start off. [caption id="attachment_149077" align="alignnone" width="300"] White to move - T.R. Dawson[/caption] Black decided to resign here and it’s easy to see why. 1.g7 Qxg7 2.hxg7# is inevitable. White, who was in a check, urged his opponent not to give up too quickly. Black replied,  “But I’m bound to lose, there is nothing I can do, or you for that matter .” Yet white insisted, “I bet you $100 that I can still lose this game”. So the two made the bet and white actually managed to lose! How did that happen? The answer is revealed at the end of the column. Here’s another more serious “impossible” problem: [caption id="attachment_149078" align="alignnone" width="300"] White to play and win - (Alexei Troitzky 1915) - Wait, what? Can white even give a check?[/caption] The position might seem somewhat ridiculous due to the presence of no less than five(!) dark-squared bishops, yet it is a legal position. The real problem, however, is how can these bishops checkmate the black king because there is no way white can control the light squares. In fact, if the black king insists on sticking to light squares, white can’t even give a check, let alone a checkmate. The trick is that the black king is not alone. 1.Bce5 a5 (1... Ka2 2.Kc2 a5 3.Ba1 a4 4.Bbe5 a3 5.Kc3 and reverts to the main line) 2.Ba1 a4 3.Bbe5 a3 4.Kd2 Ka2 (4... a2 5.Kc3 Kxa1 6.Kc2#) 5.Kc3 Kxa1 (5... Kb1 6. Kb3 a2 7. Kc3 Kxa1 8. Kc2#) 6.Kb3+ Kb1 7.Ba1 a2 8.Kc3 Kxa1 9.Kc2# [caption id="attachment_149079" align="alignnone" width="300"] The final position[/caption]

Mission (impossible) accomplished, almost by magic. 

The starring role played by the white king should give you a head start for the next one.

[caption id="attachment_149080" align="alignnone" width="300"] White to only move his king and checkmate in six moves - (Huddersfield College Magazine, 1877)[/caption] Can someone really deliver a checkmate by moving only the king? Apparently all it takes is a  little crusade and a discovered checkmate. 1.Kc5 Kd7 2.Kb6 Ke7 3.Ka7! Kd7 4.Kb7 Ke7 5.Kc8 Kf8 6.Kd7# In terms of sheer paradoxicality, the first move of the following ‘impossible’ study has next to no equals. The composers borrowed the idea from the famous Reti maneuver, but went one better with their prelude and execution. [caption id="attachment_149081" align="alignnone" width="300"] White to play and draw - A & K Sarychev (1928)[/caption] It is easy to see why this fits comfortably under our criteria of impossible problems. The obvious  try 1.c8=Q does not work because of 1…Bf5+ 2.Kc7 Bxc8. If white maintains the status quo with 1.Kd6, black wins after  1... Bf5 2.Ke5 Bc8 3.Kd5 Kf4 4.Kc5 Ke5 5. Kb6 Kd6. Surely, if those two attempts fail, white’s cause is as impossible as they come? But as a famous fictional detective once said, once you eliminate the impossible, whatever remains, no matter how improbable, must be the truth. So what remains? 1.Kc8!! It is no wonder that our mind rebels against such a counter- intuitive move. We block the path of our only saviour (the passed c-pawn), while allowing the enemy pawn a free run. It takes a while to understand why it works. 1...b5 (1... Be4 2. Kb8 and white draws) 2.Kd7 b4 (2...Ke4 3.Kd6 Bf5 4.Kc5 Bd7 5.c8=Q Bxc8 6.Kxb5) Now the Reti maneuver is used, with the white king closing in on two fronts at the same time. 3.Kd6! (The tempting 3.Ke6 is a mistake in view of 3...Ke4!) Bf5 4.Ke5 4...Bc8 5.Kd4 Be6 6.c8=Q Bxc8 7.Kc4 and the impossible is achieved. A truly amazing composition. Back to the very first problem, white of course lost the bet, not the game!  Sorry about that.