47.Nxb6+ suggests itself, but 47...Bxb6 in reply stops the pawn, and trying to zug the bishop thereafter doesn't look hopeful.

So maybe 47.Ba5, pinning the knight against the bishop? If Black's king comes back with 47...Kc6, then 48.a7 Kb7 49.Bxb6 overloads the king and 48...Na8 49.Nb8+! protects the knight as Black is unable to protect his bishop.

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If is very hard to get Black's knight out of the way. Black will bring his king back to b7, and White will be hard-pressed to protect the pawn.

47. Ba5 Nxd7 (else: Black loses one piece)

48. a7 Nxe5
(48...Bxa5 49. a8=Q+ Kxe5 50. Qxa5 1:0)

49. Ke2 (or Kc2; in any case a white square were Black has no check next move, neither wirh bishop nor with the Ne5)

49...Bxa5 50. a8=Q+;

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Although there are few pieces on the board, this puzzle is far, far tougher than many we've seen lately. For this paradox we can thank the nature of minor piece endings with advanced passed pawns: Suddenly, material value takes on entirely new, and often apparently enigmatic, meanings.

(This is reminiscent of a blitz game I played, years ago, against an extremely tough Afghani named Farouq, who although his rating was only in the 2100s was very quick and solid, fought like a lion, and was consequently difficult to beat in fast games.

Both players had two knights, a bishop and some advanced passed pawns on the queenside, with the kings somewhat out of play on the other wing. I had an extra pawn, but Farouq's passed c-pawn was more advanced than my corresponding b-pawn.

On autopilot, I attacked his bishop with one of my knights, threatening to take it for nothing with check. But Farouq brilliantly ignored this empty threat and pushed his c-pawn, realizing that if I wasted time picking up the bishop, I wouldn't get back in time to stop the pawn. Eventually, I was forced to sac the knight to stop the pawn.

But turn about is fair play, and now it was my turn. I pushed my own b-pawn, and finally Farouq, in turn, had to sac a piece to stop it. This left us in a far simpler ending, and I was still a pawn ahead and went on to win.)

Now back to the puzzle:

My first inclination, having seen that 47. a7 goes nowhere after Black screws his knight into a8, was to pin the knight with 47. Ba5, and it appears that this works, although in seemingly mysterious ways:

<47. Ba5!...<>>

Now White threatens to win a piece, and will do so on the immediate 47. ...Na8?, forcing the king to come back to defend.

(Of course, 47. ...Nxd7? is out of the question, for after 48. a7, Black can't stop the pawn.)

<47. ...Kc6
48. a7...<>>

Again, Black has only one defense. Taking the knight with either king or knight loses, the latter to an immediate pawn push, the former to an exchange on b6 followed by a pawn push. Stopping the pawn is more important than trying to win a piece, so:

<48. ...Na8!<>>

This does not lose a piece because White's knight is also hanging.

<49. Bxd8, Kxd7
50. Ba5...<>>

The point: Although the pawn is blocked and material is even, the black knight is corraled by the bishop long enough to secure a win on the kingside.

<50. ...Kc6<>>

Black needs to keep the king near the pawn. If he goes to e6 to hold his kingside pawns, the white king penetrates on the queenside and traps the knight, freeing the bishop to stop counterplay while the trapped knight is picked off and the a-pawn advanced.

<51. Ke4, Kb7<>>

To advance the pawns at this stage only weakens them, easing White's task.

<52. Kf5, Kxa7
53. e6, fxe6†
54. Kxe6, Nb6
55. Kf7 <>>

I'd have to spend some time proving the win, but this appears stronger than exchanging on b6. The king-and-pawn ending looks like a draw after 55. Bxb6†, Kxb6; 56. Kf7, g5!; 57. Kf6, Kc6; 58. Kxg5, Kd7, and Black's king reaches c7 in time to achieve one of the known king-vs.-rook's-pawn draws, in which White will ultimately have the unpalatable choice of stalemating Black or being stalemated himself.

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Now if 49. Bxd8, I'm struggling to see a clear win for black. But what about 49. Nb8+?

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Black cannot protect the Bd8 and so will lose a piece. 49...Kb7 50. Bd8 Kxa7 51. Nc6+

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You're right, of course. I looked at that idea briefly, but for some reason gave it short shrift. But it does work, and very well: The White knight gets back out to shred Black's kingside pawns; better, its opposite number on a8 remains a prisoner there, looking on as the distant foot soldiers are turned into mincemeat by the white armored cavalry.

Neither did Henry V at Agincourt. That's why he held back in difficult terrain and waited for the French men-at-arms to charge his position, with disastrous results.

Had he gone into "open" warfare in smooth terrain, his archers would have been overrun before they had a chance to make a fight of it.