One day I was writing a column on trapped pieces. I wanted to point out that you don't need to always capture the opponent's trapped knights in the corner right away, and neither should the trapped knight always sacrifice itself for a pawn.
So I fooled around creating several simple endgame positions which might examplify this theme, when I suddenly stumbled across a position that the computer said was winning for White. At first, I did not at understand why, but it turned out to be an amazing and beautiful problem. Before proceeding, I strongly suggest you try to solve this apparently simple endgame, White to play and win:
OK, now that you have tried it on your own, let's walk you through the solution. Clearly 1.Nxb6 axb6 will just win for Black, so sacrificing the knight for the pawn is senseless as is running White's king around to the queenside without going after the black pawn on e6. But it is also key that Black cannot just guard his e-pawn, as then a knight sacrifice will work:
Therefore, it should now be clear that Black has no choice but to race with White. After 1.Kg5 then 1...c5! is forced, as is 2.Kf6 b5 3.Kxe6 c4, bringing us to this position:
White now has a choice to capture or not on c4. Let's assume he does not. Then it looks like a race between White's e-pawn and Black's c-pawn, but where should White's king go to get out of the way? The most aggressive square is 4.Kd7. Now if Black is greedy and plays 4...cxb3?, White checkmates with 5.e6 b2 6.e7 b1Q 7.e8Q+ Kb7 8.Qc8#
...So 4...cxb3? is terrible, but if Black defends correctly with 4...c3, how can White win? The most straightforward try, which almost everyone attempts, is 5.e6 c2 6.e7 c1Q 7.e8Q+ Kb7 when the black queen on c1 stops the checkmate on c8 that we experienced in the previous line:
It turns out White cannot make progress on this line, even ahead a knight - try it and you will see! The knight is trapped in the corner and Black is always threatening to check White forever. But how can White improve, and where?
Amazingly, after 4...c3 White has the strange-looking 5.Nc7! But how does that help? After 5...c2 Black will promote first, so how can White possibly win? You might notice that 6.Na6+ is tricky because Black cannot play 6...Kb7? due to 7.Nc5+ and 8.Nd3 holding c1 just in time! Then White would win by promoting his e-pawn. So Black must respond to 6.Na6+ with 6...Ka8, but what can White do then?
Here's real the real beauty lies, and what makes this problem difficult to visualize (from the starting position) for even your expert and master-level friends and mentors - you are sure to have some fun showing them this problem and seeing if they can find the answer without moving the pieces
[Drum roll now...] The key is that White must play the paradoxical 7.Kc8!! allowing Black to promote with check! After 7...c1Q+ the key is 8.Nc7+ which is not smothered mate, but does force Black to give up his hard-earned queen with 8...Qxc7, when White easily wins the race and the game with 9.e6. Isn't that the kind of beautiful and unexpected pattern that makes chess challenging and fun?
I asked my wife Shelly to put this problem on my gravestone